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CORNELL
UNIVERSITY
LIBRARYANALYTICAL ESSAY
ON THE
GONSTRUCTION
OF
MACHINES
CranslateU front tlje ^rcttd»
M. M. LANZ & BETANCOURT.
Honfton;
PUBLISHED BY R. ACKERMANN, 101, STRAND;
AND MAY BE HAD OF ALL THE BOOKSELLERS IN THE UNITED KINGDOM.
DIGGEN5, PRINTER, SAINT ANN’s UNE.
• •\
1FBEFATOHY ADDRESS.
THE state of perfection which the manufacturing
Arts have attained in this country may be traced to the
general Advancement of Science which has distinguished
the present Age. Hence, \vc must look for a continuance
of improvement by a proportionate progTess in scientihc.
Knowledge; and every attempt which has that object
in view, and is executed with adequate ability, has a
rightful claim to the grateful sense of the age and country
in which it has been produced.
This observation might be thought sufficient to justify
the introduction of any foreign work of general Utility to
the attention of the English Nation, by cloathing it in
the English Language. But the Editor presumes to take
an higher ground in favour of this Volume from the great
Utility of its subject and the Novelty of its Execution.
An Elementary work that brings a mass of important prac-
a 2PREFATORY ADDRESS.
tical information within the circle of early studies; that
may be considered as a Grammar in the Science of Me-
chanics; is so arranged as to be perfectly intelligible to
that invaluable class of Socie ty, the practical Artisans,
and at the same time may be a useful volume of reference
to the more learned Classes, cannot but be considered as
a useful and consequently an acceptable addition to the
British Library; as it will transmit to this country the
honour wliich the Author has established in his own.dyne/rte-allat/ea/mtcdxreMtr/meveme/Mt, efiyo/aymp a	a/Mra/u^Mr, arrun?eefunMer	ofrecti&ntar. exreetfor, foMer cu/t/tinear nwveme// fo, fcsuiM/itit/et/info /irert &*t/fertiet/e metums, llfofitnfforrnecriJf/riaMt’ re/cctli?*.
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^r/rOrat at j?^?e&ervn,<z**' vi itAegne/>Ai r fre/sTABLE of CONTENTS.
PREFJTORY JDDRESS...................................................Page
i '
Introductori/ Remarks and Explanations................................1
SECTION I.
To convert direct and cquable rectilinear motion, or the velocity of xohich is variable by a
given law, inio direct rectilinear motion, ofvelocity similar to that of the moving power,
either equable, or variable by a given law ; and in the same, or in different directions .	3
SECTION II.
To convtrt a given direct and equable rectilinear motion, or the velocity of which varies
a given laxo, into alternate rectilinear motion of velocity similar to that of the
moving power, either equable or variable by a given law; and in the same, or in different
directions	......................... 3
SECTION III.
To convert a given direct and equable rectilinear motion, or the velocity of which varies
by a given law, into direct circular motion of velocity similar to that of the moving
power, either equable* or variable by a given law; and in the same, or in different
directions •	...........-..............................13
SECTION IV.
To convert a given direct and equable rectilinear motion, or the velocity of which varies
by a given law, into alternate circular motion of velocity similar to that of the moving
power, either equable, or variable by a given law; and in the same, or in different
directions..................................................................2$CONTENTS.
SECTION V.
Page.
To convert a given direct and equable rectilinear motion, or the velocity of which varies by
a given [law, into a direct curvilinear motion of velocity similar to that of the moving
power, either equable, or variable by a given law; and in the same, or in different
direct ions......................................................................31
SECTION VI.
To convert a given direct and equable rectilinear motion, or the velocity of which varies by
a given law, into an alternate curvilinear motion, of velocity similar to that of the
moving pozoer, either equable, or variable by a given law; and in the same, or in dif-
ferent directions....................................................................ibid
SECTION VII.
To convert direct and equable circular motion, or the velocity of which varies by a given law,
into alternate rectilinear motion of velocity similar to that of the moving power, either
equable, or variable by a given law; and in the same, or in different directions .	.	. ibid
SECTION VIII.
To convert a given direct and equable circular motion, or the velocity of which varies by
a given law, into direct circular motion, of velocity similar to that of the moving
power, either equable, or variable by a given law; and in the same, or in different
planes...............................................................................73
SECTION IX.
To convert direct circular motion, of uniform velocity, or which varies by a given law,
into alternate circular motion, of velocity either equable, or variable by a given law ;
and in the same, or in different directions................................91
SECTION X.
To convert direct circular motion of uniform velocity, or which varies by a given law,
into that of a curve of given species, direct and continuous, of velocity similar to that
of the moving power, either equable, or variable by a given law; and in the same, or
in different planes of direction  .........................................117CONTENTS.
SECTION XI.
Page.
To convert direct circular motion of uniform velocity; or which is variabit according to a
given law, into alternate motion in a given curve, of vclocity similar to thatofthe
original motion, cither equable or variable according to a given law; and in the same,
or in different planes of direction................,.........................................134
SECTION XII.
To convert direct motion in a given curve, and of velocity either equable, or variable by
a given law, into alternate rectilinear motion; of velocity similar to that of the original
motion, either equable, or variable according to a given law; and in the same, or in
different planes qf direction.  ...........................................133
SECTION XIII.
To convert direct motion in a given curve, and of velocity either equable, or variable by
a given law, into alternate circular motion; of velocity similar to that of the original
motion, either equable, or variable according to a given law; and in the same, or in dif-
ferent planes of direction. ...............................................ibid
SECTION XIV.
To convert direct motion in a given curve, and of velocity either equable, or variable by
a given law, into motion in a given curve ; of velocity similar to that of the original
motion, either equable, or variable according to a given law; and in the same, or in
different planes of direction ...................................... .ibid
SECTION XV.
To convert direct motion in a given curve, and of velocity either equable, or variable by a
given laxv, into alternate motion in a given curve, of velocity similar to that of the
original motion, either equable, or variable according to a given law; and in the same
or in different planes of direction......................................13$
SECTION XVI.
To convert alternate rectilinear motion, of velocity either equable, or variable by $ given
law, into alternate rectilinear motion, of velocity similar to that of the original motion,
either equable, or variable according to a given law; and in the same, or in different
planes of direction...............................*.................... • ibidCONTENTS.
SECTION XVII.
Pagg.
To convert alternate rectilinear motion, of velocity either equable or variable by a given
law, into alttrnate circular motion, of velocity similar to that of the original motion,
either equable, or variable according to a given law; and in the same, or in different
planes of direction	.  .......................................................137
SECTION XVIII.
To convert alternate rectilinear motion of velocity either equable, or variable by a given law,
into alternate motion in a given curve, of velocity similar to that of the original motion,
either equable, or variable by a given law ; and in the same, or in different planes of
direction	............... 153
SECTION XIX.
To convert alternate circular motion, of velocity either equable, or variable by a given law
into alternate circular motion, of velocity similar to that of the original motion, either
equable, or variable by a given law ; and in the same, or in different planes of direction iJbid
SECTION XX.
To convert alternate circular motion, of velocity either equable or variable by a given law,
into alternate motion in a given curve, of velocity similar to that of the original motion,
either equable, or variable by a given law; and in the same, or in different planes of
direction .......	* ...	* .	* ..........................155
SECTION XXI.
To convert alternate motion in a given curve, of velocity either equable or variabit by a given
law, into alternate motion in another given curve, of velocity similar to that of the ori-
ginal motion, either equable, or variable by a given law ; and in the same, or in dif-
ferent planes of direction ............158AYALYTICAL ESSAY
ON THE
CONSTRUCTION OF MACHINES.
nature of the mechanical movements which occur in the construction
of maehines, may be classed in three divisions, viz. rectilinear, circular,
and those which are regulated by other given curves, and the subjects of either
of these classes will again arrange themselves, under the distinet heads of direct
and alternate motion.
Fifteen different arrangements may therefore be made of those motions by
combining them in pairs, or twenty-one different arrangements, by combining
each with each. The object of ali mechanical arrangements is either to
communicate some of those motions, or, by combining and transposing them
to produce any required conversion of them.
The Synoptical table (Piate 13) affords a perspicuous display of the best
examples of these several motions. It is composed of twenty-one equal horizontal
tanges of square compartments, each of which contains one example; each
range is distinguished by numeral figures, and each vertical column by Roman
capitals, the intersection of two columns or the situation of any given example
is therefore indieated by a letter with an affixed numeral, i e, the distinguishing
letter of the vertical column and the numeral of the horizontal range. The
open spaces which occur in some parts of the table from the greater abundance
of examples in other of the ranges, are evidently unavoidable from the nature
of the arrangement, they may however not improperly be considered as
B2
reserved to register those future discoveries and inventions which tlie researches
of practical and scientific tnen may be expected everywhere to produce.
In order to confine the table of contents within convenient Iimits, and avoid
the disagreable effect of frequent extensive ranges of open spaces, whenever
the number of examples occurring of one class, have exceeded twenty, the
remaining subjects have been arranged in a supplementary range, immedi-
ately below the iirst, and distinguished by the sarae numeral figure with the
addition of a line, as in the ninth range, where the supplementary range
(which became necessary frorn the number of examples) is marked 9'; And
whenever the conversion of one given movement to another is not immediate,
but must be effected by a preparatory conversion to some other movement
then a single line of explanatory description is introduced in place of the
horizontal range of examples, as in range 2, which should contain examples
of alternate rectilinear motion, as produced by conversion from direct recti-
linear motion: here the required conversion is not immediate, but is to be
effected by the preparatory conversion shewn in the 3rd range, which the
line of explanatory description accordingly refers to.
To avoid useless repetition, the lst compartment of an horizontal range
is sometimes occupied by a concise reference to movements which are to be
found in other parts of the table, and which might also have been placed
in that column, eitlier in the state in which they are found by that reference,
or modified by the intervention of another, as in column 4, where direct
rectilinear motion is required to be converted into alternate circular motion:
bere the first compartment of the range informs us that if the given rectilinear
motion be first converted into direct circular motion by some of the metliods
exhibited in the 3rd range, reference from thence to the 9th range will furnish
the required conversion.
Each horizontal range of examples, furnishes the subjects of description
of asection of the work, in which the object of each combination is explained,
with the general solution of the problems analogous to the conversion required;
The particular modes of execution with which we are acquainted are shewn
by reference to the sources of information, and considerations are added on3
the valae of such means, and the various practical applications which may
have been made of them.
The subjects of the general table or index piate (Piate 13.) are also drawm
to a larger scale, in which each subject has the literal and numeral charactere
prefixed which point out its situation in the index piate, as for instance, the lst
figure of piate 1, is distinguished in that piate, and referred to from the index
piate by the designation B 1, which explains its situation in the index piate to
be the intersection of the lst horizontal rangc with the vertical column B.
Eight of these subjects are arranged in each piate, and each has its respective
letters of reference for the description. We have also been obliged to introduce
. some auxiliary examples in a distinet piate (No. 12.) which do not arrange
themselves in the index piate.
SECTION. I.
To convert direct and equable rectilinear motion, or the velocity of which is
variable according to a given law, into direct rectilinear motion of velocity
similar to that of the moving power, either equable, or variable by a given
law, and in the same, or in a different direction.
i
THE only first movere the mechanical action of which can be considered
as being direct and rectilinear, are lst the Air—either by its motion, its gravity,
its elasticity, or its rapid expansive force. 2d. Water—either by its motion, its
gravity, its re-action, or by the expansive power of steam. And 3d. Gunpowder—
either by its explosive force, or its re-action, as in the instance of the common
rocket *.
* Examples of the instantaneous expansion of air, by the combustion of gunpowder or other com-
bustible substances, applied as first movers, may be found in the Repertory of Arts and Manufactures,
rol. i. p. 154; and in vol. vi. p. 100, a memoir on the subject by Bramah. In the works of Jean de
Haute Fenille, printed at Paris 1694, is also a memoir under the title “ Pendulle perpetuelle ;—la
maniere d’elever l’eau par le moyen de la poudre a canon, &c.” We find the Academy of Sciences
engaged at that time in adapting this power to raising heary bodies. And the author has proposed an
hydraulic telegrapb, in which he believes is the earliest idea of communicating the action of a power to
B 24
An endless rope, moving about two fixed pullies may exemplify rectilinear
motion, which is in fact, but direct motion in a circle whose radius is infinite.
The progress of a body in a direct line between two given points, either
by its own motive powers, or by the action of any first mover, is a more
distinet example of rectilinear motion. The arrangements of the art of marine
rigging afford many instances, and all those engines which act by means either
of simple or combined pullies.
The arrangement B1, and C1, of piate 1, exhibit the most familiar instances of
this proposition:—D 1, E 1, F 1, G 1, HI, K1, are exaraples of parallel motion.
(A 1.) Index piate. (Piate 13.)
If circular motion be produced from rectilinear by the methods exhibited in the
3rd range, different examples of the required conversion may be found in that
range.
(B 1.) (B 1, 2nd figure.) Plan and Elevation—Piate I.
The points a and b are reciprocally required to traverse tbr respective spaces
a b and c d with the same given velocity.
A general solution of this problefh may be afiorded by a simple pulley e,
(fig. B 1,) or by two such pullies, if the given points are required to move in
different planes (B 1. 2nd fig.)
(Cl.)
Problem 2. This is a repetition of the last problem, but with the condition
that the distance traversed by c, is less than that of a, in a given ratio.
A general solution of this problem is afiorded by the combinations of pullies,
which are usually adopted for the purposes of lifting heavy masses. These
expedients are too well known to need minute explanation, but many examples
worthy the attention of mechanics may be found among the machines approved
great distances by means of long tubes filled with water. A report by Bertliollet and Camot, upon a
machine invented by Messrs. Niepce, will be found in the Memoirs of the first class of the Institute for
1817, page 146, these gentlemen term their machine C( Pyreolophore,” and apply the instantaneous
expansion of air by combustion, as a first mover.
Applications of the pressure of water or of the atmosphere, as first movers, may be seen in aLes Annales
des Arts et Manufactures,” vol. xiii. page 209, by 0’Reylli. A description of the engine of Schemnita;
the improvements proposed in it by Boswell; and a description of Goodwyn’s machine.5
by the Academy of Sciences; in the work of Sabaglia; and in all those autliors
who have written on the art of rigging maritime vessels.
(D 1.)
Problem.—To move a line continuallyparallel to itself. This motion is familiar
to us in its applicatioris to the common parallel rule used in geometrical
drawing *.	•	•
(EI.) '
This is another application to a more commodious construction of the parallel
rule: some useful applications of it have also been made by M. Ramsden f.
(FI.)
The foregoing examples are in general not well adapted to works of consider-
able size, or where great accuracy is required. In our cotton spinning machinery
\ve find however a very elegant and satisfactory specimen of a parallel motion:
In this machine a platform which carries the spindles, and is from 18 to 27 feet
in length, is required to traverse over a space of about five feet, and to retain
in its path an accurate parallelism. The most costly and complicated means
had been exhausted to effect this, when it was at length accomplished in a
nanner at once so simple and correct as exceeded all that eould have been
expected. In the figures, B represents the carriage or platform running on four
wheels a a-a a, upon this carriage is placed a set of spindles, which receive their
rotatory motion by the means shewn at G 8 of the table; d is the point to
which the moving power is applied. The required constant parallelism of this
machine seems extremely difficult to effect, from its considerable length, it is
nevertheless obtained in a very perfect manner, by means of two cords nmpq,
and rstu, the first of these nmpq passes over two pullies s m, and the
ends n q, are fixed. The second cord rstu, also passes over two pullies,
placed respectively over those already mentioned, and its ends r and u,
are also fixed. It is necessary that the attaching points u q and n r, of the
* See the work of James Leupold, entitled (( Theatre de 1’Arithmetique et de la Gcoroetrie,'5
1727, piate xii. fig. 4.
+ See the same work, piate xii. fig. 6.6
two cords should be so situated as to stretch the cords perfecti y parallel to each
other, and with equal tension; and the carriage B, should be placed at right
angles to them. These arrangements are easily practicable, and the effect
is as perfect as can be conceived.
(Gl.)
A solution of this problem will also be obtaiued by the motion of a ruler
a b, which runs on two fluted cylindric wheels or rollers c and d, placed near
to its ends. It is necessary that these rollers should be precisely of equal
diameter, and be so placed that their faces shall be perfectly parallel. This
instrument preserves its parallelism merely by the friction produced by its own
weight on the surface on which it rolls: but in the application of this movement
to machines of considerable power, as in the instance of that which is used in
boring artillery, it is necessary for the rollers to be deeply indented, for the
purpose of engaging in hooks, which are fixed to a massive frame. To this ruler
is sometimes added a dial, on which its progress is indicated, so that parallel
lines may be described at any required distances.
(H I.)
Let A be a wedge which is at liberty to slide longitudinally between four
upright pillars cd ef, while a second wedge B, is so confined to the pillars by
projecting pins, or friction rollers, that it is at liberty to move in a vertical
direction only. It is evident that if under this arrangement the wedge A receives
a motion in the direction f d, the upper wedge will be gradually raised, and
the side n m, will move continually parallel to itself: we find this arrangement
of wedges frequently applied to useful purposes, among others, to the pedals
of musical Instruments; but it appears capable of more extensive and useful
application. M. De Bettancourt adopted it in England with complete success,
for the purpose of raising the lower cylinder of a flatting engine; and he conceives
that strait lines might be divided by this means, with as much accuracy as is now
obtained with respect to circles by means of the present dividing piate. If we ima-
gine the moving power to act constantly in the direction fd, ofthe base ab ofthe
lower wedge, and that an arm or ruler lp, situated at right angles, to the inclined
plane cb, and having friction rollers at the extremity 1, it will rest on the7
inclined plane, and the ruler will slide between the two projections o and q.
The inclination of the plane being arbitrary, it is evident that a direct rectilinear
motion may produce a similar motion in a given angular direction with it, and
the velocity of the first will be to that of the second, as radius is to the sine
cba. If the angle cba be reduced to o, the rule or bar 1 p, will remain
immoveable. This will be the case wlien the original rectilinear motion is
converted into a rectilinear motion at right angles to it. These results are
obtained by the help of the second wedge B, as already described ; and if a
third be added, which shall be attached to the second, both the direction of
the movement and the relative velocities may be changed at pleasure. The
line cb, may also be eurved at pleasure, in which case the direct rectilinear
motion will produce an alternate rectilinear motion, and the arrangement would
be classed among those of Section II.
(II.)
Is the Hydraulic Ram of Montgolfier. A description of this engine may be
found in the Repertory of Arts, volume 9; in the Journal de l’Ecole Polytech-
nique, volume 14; in the Journal des Mines, numbers 48, 64 and 66; in the
Journal de Physique of February 1798; in the Bulletin de la Societe d’En-
couragement, Numberl9; Number 61, of the same work for July 1809, also
contains an article on some improvements of the Hydraulic Ram.
A current or fall of water which we have considered as a first mover, acting
with an uniform velocity and directly rectilinear, produces an alternate move-
ment in a valve, and with the addition of an air vessel will afford a continued
jet of water; and which we have also considered a direct rectilinear motion.
(Kl.)
This is another method of producing a motion which will preserve a constant
parallelism: it is frequently uscd in the drawing instrument familiarly known
by the name of parallel ruler, and may be seen in other applicatfons in Leupold’s
Theatre de l’Arithmetique et de la Geometrie, fig. 5, piate 12. Parallel rulers
on this construction are frequently introduced in cases of mathematical drawing
iustruments.8
(Ll.)
A B is a flat bar or ruler, having a longitudinal passage cut through it
from n to m. A small fixed cylinder c, is made to enter this passage without
having any motion through it. C D is a bar which is allowed to slide easily
between the two small clips p and q; and it also carries an upright arm E F,
from some part of which at any distance from the bar C D there rises another
small cylinder a, which also enters the longitudinal passage n m of the bar AB,
but on the opposite side to the first mentioned cylinder c, and so that they
do not come in contact with each other when the bars are in motion.
If the bar A B be made to move so that its end A shall take the direction of
the right anglc A G parallel to the bar C D, the point a, will in the same time
traverse the right line a b.
It will be seen thus, that by the direct or alternate rectilinear motion of the
point A, we may communicate to the bar C D a motion of the same kind,
with a velocity of any required ratio, or even inversely, by arranging the
cylinder a in the arm E F, in a suitable manner.
SECTION II.
To convert a given direct and equable rectilinear motion, or the volocity of which
varies by a given law, into alternate rectilinear motion of velocity similar to
that of the moving poioer, either equable or variable by a given law ; and in the
same or in different directions.
THE given rectilinear motion will be converted into circular, by the methods
shewn in Section III.; and the examples of Section VII, may then be taken
as examples of the required conversion.
Having considered a fall of water as an uniform rectilinear motion, if we
imagine a vessel which is alternately filled with the water, and emptied of it
by means of a syphon, a float enclosed in the vessel will rise and fall alternately.
This mover may be seen in a work entitled " Utilissimo trattato dell’ Aque cor-
renti, &c.” dal Cavalier Carlo Fontana. Rome 1696.9
An application of it as a mover, has been made by Messrs. Bossu and Solage,
in a model of a corn mill deposited in the Repository of Machines: but in
this instance, instead of using a syphon to empty the vessel, the valves of supply
and exit are opened by the motion of the float-rods. We are not aware of
the reasons which determined those distinguished machinists to convert the
alternate rectilinear movement of the float-rod into an alternate circular
motion ; and thence to a direct circular motion, rather than avoid the use of
an useless intermediate movement, which so materially lessens the power of
the engine *.
The steam engine, in which steam may also be considered as a power con-
stantly acting in a rectilinear direction, and producing the alternate movement
of the piston. Hydraulic pumps, such as are some of those used in the Hungarian
mines, in which a column of water acts on a similar principle, and produces the
same effect as steam in the steam engine. Those in which the sudden expansion
of air by a rapid eombustion, is used as a first mover. AU these machines
should be classed in this division of our work, although not perhaps in a direct
manner. But as the changing the direct rectilinear motion of the moving power
into the alternate rectilinear motion of the piston, frequently involves considerable
complexity of means, we consider such instances rather as particular machines,
than those simple elementary transformations which it is our immediate business
to describe; and therefore we have deemed it sufficient to mention them.
The alternated movements exhibited in ali bodies which are exposed to
considerable changes of temperature, and more particularly the metals, may be
ranked among the most powerful first movers. It frequently counteracts the in-»
tention of the mecbanical artist, and requires the exertion of all his patience and
* The motion of a float is used in. the boiiers of steam engines, or in reservoirs, to maintain the level
of the water within certain limita. ... -iVArchitecture Hydraulique of M. De Prouy, toI. 2, contains
the description of a method of regulating the velocity of steam engines by means of a float furnished with
a syphon, invented by M. De Bettancourt.
A description of an instrument invented by M. Solomani, for the purpose of preserviog a' given
temperature in a receiver of water by means of an areometer, which acts as the float, may be seen in L’art
du distillateur des eaux-de-vie et des esprits, par M. Le Normand,
C10
ability: his ingenuity when thus excited, however, devises the means not merely
of extrication from the difficulties of the subject, but even in many cases converts
them to his advantage. Remarkable instances may be traced iri the contrivances
adopted to neutralize the action of this mover in many of our horological
machines; and the inconceivable precision obtained in the admeasurement of
trigonometrical bases, by means of the metallic rods of M. Borda*. Among the
Instruments whose action depends on this property of expansion by encreased
temperature, the thermometer of M. Brequet should be eminently distinguished.
This alternate movement has been tumed to useful account in regulating the
draught of furnaces. A very elegant application of it has also been made by
M. Molard, to the adjustment of two walls in one of the galleries of the Repository
of Machines f.
(A 80
The oscillating column of M. Mannoury d'Ectot.
' This machine resolves itself into two cylindrical tubes A and B, placed verti-
cally, one immediately'above the other; they are separated from each other
by a small interval. The upper extremity of the tube A is closed by a piate,
in which is a circular aperture d d, corresponding with a similar aperture in the
tube B. C is a circular piate or diaphragm of smaller diameter than the aperture
dd, and is placed a little below it. The action of the machine is thus:—The
tube A being constantly supplied with water by a convenient reservoir, it will
escape by the annular opening formed between the circular aperture d d, and
the diaphragm C, and with the velocity proper to a column of water of uniform
altitude. The annular aperture by which the water escapes encreases the usual
contraction of the spouting fliuid, and forms a conical portion of water: the
apex of which, by a due adjustment of its distance from the tube B, must be made
to reach a little way within it.
A conical portion of the iluid will remain stationary upon the diaphragm.
* All the works on clock and watch-making contains examples of such arrangements.—Delambre.
Base du system metrique.—Bulletin de la societe (Tencouragoment, No. 48, June, 1808.
+ Borgnis. Traite du mouYement des fardeaux.II
The water rushes into the tube B, and if it be cylindrical will rise in it to a height
equal to one third more than the altitude of the column in the tube A, but if it
be conical the altitudes will encrease with the convergency of the cone. When
it has reached its maximum of elevation, it descends, passes into the stationary
portion f, and causes the running portion of the fluid to diverge and to project
a paraboloidic sheet, through the separating interval of the two tubes until the
tube B is entirely empty. The jets of water recover their original action; the
contraction of the spouting portion of the water again takes place; and the
same process is recommenced. This alternate movement is found to take
place in equal times.
The noble inventor expects to apply this alternate rectilinear motion of
water to useful purposes as a mover, and to render the engine itself preferable
to a great number of those generally used for the purpose of raising water.
A work descriptive of this nobleman’s ingenious inventions is expected shortly
to make its appearance.
M. Carnot, in his report to the Institute of the 28th December, 1812, upon
the different hydraulic machines presented by M. Mannoury, States the general
problem proposed by that gentleman to be—From a given fall of water to
elevate a portion of it above the reservoir by means of a machine, all the parts of
which are absolutely fixed; and which, consequently, does not comprehend or
require either levers, wheels, pistons, valves, or any other moving parts of what-
ever description.”
M. Carnot explains the entire novelty of this proposition, and gives an account
of the principal methods which have been successfully adopted by the author
for its accomplishment: speaking of the oscillating column he says—f ■ Of these
methods, this appears to us to possess the most novelty, because we are not
acquainted with any facts which could have suggested the fundamental idea.’*
He explains the phenomen® by reference to the principies of the forces of activity
of bodies in motion, and closes his report with a well-merited eulogium on the
intelligence and learning of the noble author,
c 2SECTION III.
To convert a given direct, and equable rectilinear motion, or the velocity of which
varies by a given law, into direct circular motion, of velocity similar to that of
the moving power, either equable or variable by a given law, and in the sarne
or in different direclions.
THE re-acting engine of Segner gives a direct solution of the problem ; and
Mour’s centrifugal machine, noticed by Eulcr, in the Memoirs of the Aeademy
of Berlin, for the year 1751, gives a solution of the inverse problem ; both these,
therefore, class themselves in this Section.
(A3.)
A cylinder having a motion on its axis, and a rope winding on its surface,
gives a general solution of this, and the inverse problem. The arrangement is
sufficiently familiar to render a more detailed description unnecessary.
(B3.)
The cord used in the preceding movement is here superseded by an endless
chain furnished witli projecting teeth, which engage in a toothed wheel, affixed
to the end of the cylinder.
(C 3.)
A NUT AND SCREW.
If the nut of a screw be fixed, and the screw be turned within it, the screw
will have a motion which is composed of its own rotation on its axis, and the
conversion to direct rectilinear motion. Thus it is used in the arts to penetrate
hard substances—to draw or force them together—to lift heavy burthens—and in
some of the tools of watchmaking, as drills. The axis of the drill is so placed
that its ends are supported by two screws, the nuts of which are confined or
held between the puppetsof a lathe. The two screws being turned by this
means in opposite directions, communicate to the drill the required rectilinear
motion. Another method, which is much to be preferred, is to support the drill
by two Steel cylinders which pass through the puppets of the lathe, and close to13
these are placed two screws, the nuts of which are also held by the same
puppets. The heads of the screws are in this case of sufficient size to press
against the ends of the two cylinders which support the axis of the drill; and
when turned ia opposite directions gives to the drill the required motion, and
in a more steady manner than was afforded by the preceding method.
If the screw be turned without being suffered to change its place, the nut
must not be allowed to turn, but to have liberty to move in the longitudinal
direction of the screw, and in this case the circular and rectilinear movements
are divided, and a direct solution of the problem is obtained: the circular move-
nient being converted into rectilinear. A rotatory motion of the screw may also
be produced by giving the nut a rectilinear motion, but the friction of this
motion is so considerable that it is seldom practised.
It is frequently required to hold a screw and its nut together, so that no change
of their relative positions may take place by accident, carelessness of workmen,
or by auy violent motion or shock which might be produced by the machine;
this is eflected iri a very simple manner by means of a second nut, which screws
close upon that which is required to be fixed; the first nut is thus continually
pressed forward in the longitudinal direction of the screw by the second nut,
and the friction between the first nut and the screw, being as already observed,
very great, the action exerted is not sufficient to overcome the resistance; the
re-action of the nut, which is pressed upon, operates upon the tightening nut,
and the resistance encreasing with the pressure, they both become fixed.
The screw is one of the mechanical powers of the most general use in the arts;
there are few in which it is not rendered useful, and it varies its character of
usefulness: sometimes having relation to the mechanical composition of the
instrument, sometimes to the purpose for which it is to be used.
An arrangement of two screws placed parallel to each other is frequently used
to produce the parallel motion of a plane of considerable length.
Presses for different purposes are constructed on this principle. In the 4th
volume of the machines approved by the Academy of Sciences we find the appli-
catiori of the screw to the construction of a press, proposed by M. J aeques Le
Maire: the editor of that work observes, that this method of applying the14
screw is extremely ingenious, that it would be found useful in a great diversity
of ways, and will produce tbe most striking effects. He states M. Le Chevalier
De Ville to be the inventor, who employed it for the purpose of forcing barrica-
does: and has shewn the method of application in his treatise entitled—“ Traite
de Portifications de l’attaque et de la defense des places,” page 228, piate 37.
Printed at Lyons 1629. Descriptions of it will also be found in other works.
If two threads be cut on the same cylinder in opposite directions, they will
move two nuts at the same time, also in opposite directions»
(D3.)
A method of converting circular into rectilinear motion with an extremely
low velocity has been discovered by M. Prony. It is by means of this contri-
vance that wTe are enabled to avoid the necessity of usingscrews of an unusually
fine thread, to procure a slow adjusting motion. The disadvantages arising
from the use of such screws were formerly very great; the rapid wear and conse-
quent inaccuracy of the usual micrometers wras an instance of the ili consequences
produced by that circumstance. It is also capable of many other practical and
useful applications. The original idea of the inventor is extremely simple and
elegant.
A B is an axis or spindle divided into three portions ab, cd, e f The two
screws ab, e f, are of the same thread: they pass through the two fixed supports
C D, in each of which there is a nut; the spindle has an horizontal motion, and
at each revolution of the screw moves over a spaee equal to one of its threads;
the portion cd, is formed into another screw, the thread of which may either be
a little finer or a little coarser than that of the screws ab, e f, and the difference
may be small at pleasure. A nut M is introduced, in which the threads of a
micrometer are fixed: this nut being checked by the blockE P, is not at liberty
to turn with the spindle A B, which it would otherwise do: but at each
revolution of the spindle moves a space equal to one of its own threads, its
rate of motion is therefore compounded of the actual and relative advance of
the spindle AB: so that it really moves but the amount of the difference
between those motions.
This is M. Prony’s simple and ingenious solution of this problem.15
In practice it will be found difficult to make the two screws ab,, and ef, so
accurately alike, that there shall be no resistance in the nuts: one of these
might however be omitted, that portion of the spindle being in that case made
plain or cylindricaL
(E 3.)
A spiral winding about a cylinder, and exposed to a current of air or water,
■will convert the rectilinear motion of those fluids into a circular motion. The
spiral of Archimedes may be considered as the inverse of this problem *.
The process of constructing this spiral may be found in the collection of
machines approved by the Academy of Sciences of Paris, vol 7, No. 479. This
method is there proposed by M. Dubost, for the construction of a mill upon the
Rhone. In volume v, No. 338, of the same work, M. Du Quet proposed it for
the construction of a machine intended to raise sunken vessels. It is also applied
to the operatiori of tuming the comrnon jack used in our kitchens, by means of
the current of air which continually passes through the chimney; and to other
machines for the purposes of the log instrument, for measuring the progress of
maritime vessels f,
(F 3.)
Vertical water wheels, with plane floats.
(G 3.)
Horizontal water wheels, with curved floats.
(H 3.;
Over-shpt water wheels.
M. Borda in a memoir on water wheels, printed in the Memoirs of the Academy
* The theory of the screw of Archimedes may be seen in L’IIydrodynamique de Daniel Bernoulli. A
memoir by Pitot, in the memoirs of the Academy of Sciences for 1736;—another by Euler, in the
memoirs of the Imperial Academy of Petersburgh, vol. v. for the year 1754.—A work by P. Belgrado,
entitled u Theoria cochleae Archimedis; ab Observationibus, Experimentis et Analyticis rationibus
ducta, 1767.”—The premium of the BerHn Academy in 1765, adjiJdged to M. Jean Frederic Hon-
nerol •—and the work of Paucton, -on the Theory of the Archimedian screw.
+ See Theatrum Machinarum de Leupold, vol. i. pjate 51. Theatrum machinarum novum, &c. per
Gregorium AndieamBocklerum, 1662, fig.&l, S2.—Designsfor Wind and Water Mills, &c. by Jacques
deStrada, published by Octave de Strada. Erankfort, 1617, fig^ 49.16
of Sciencea of 1767, has given many important calculations on the subject,
shewing the most effective mode of applying the moving powers to such wheels,
and their effects under different circumstances; and closes his memoir with the
following reflections on the practical application of his researches.
OF VERTICAL WHEELS WITH PLANE AND INCLINED FLOATS.
Such wheels are capable of producing the half of the maximum effect, if the
floats moving in their channel exactly occupy the whole passage, allowing no
particle of the water to escape without communicating to them its excess of
velocity; but it is necessary to allow a small space sufficient to avoid the eollis-
sion of the floats with the bottom and sides of the channel; although this at the
same time allows a portion of water to escape which has not exerted any action.
It is difficult to determine the diminution of effect produced from this cause,
since it depends more or less on accuracy of workmanship; but it seldom happens
that the practical effect of such wheels is more than three-eighths of the maximum
effect,. although in theory it may be considered equal to pne half.
OF HOBIZONTAL WHEELS WITH PLANE FLOATS.
These wheels do not lose by a great deal so much of the action of the water
as the preceding ones, and should consequently be preferred where the quantity
of the fall, or other circumstances will allow the equal choice. They have also
the advantage of being susceptible of a considerable encrease of their velocity
according to its required action on the machinery to which it is applied, instead
of the constant velocity of one half of that of the current, which suits the
maximum effect of vertical wheels.
OF HOBIZONTAL WHEELS WITH CUBVED FLOATS.
These wheels have not the advantages over those of the preceding form which
theory assigns them: because in practice it is nearly impossible that the whole
of the water should enter the curves—conform to their figure—and leave them17
in an horizontal direction: all which circumstances must take place for a maxi-
mum effect to be produced. Notwithstanding these, and other defects which it
would be tedious to detail, these wheels are always of superior effect to horizontal
wheels with plane floats; and in cases where a copious or sufficient fall of water
can be obtained, they are certainly preferable to the usual vertical wheels in a
stili greater degree. For example—I am persuaded, it is perfectly practicable
to construet an horizontal wheel with curved floats; the effect of which, with
respect to a vertical wheel of the common construction, shall be at the lowest
estimation in the proportion of three to two.
OF OVEJt-SHOT WHEELS.
It is explained by M. Borda in the memoir we are now adverting to, that if a
water wheel of this class be required to produce its maximum effect, it will be
necessary to observe the three following conditions:—1. That its diameter be
equal to the height of the fall of water; or it may even be taken at somewhat
more than that dimension. 2. That the current of water shall enter the
buckets at the level of the surface of the reservoir. 3. That the velocity of the
wheeLbe exceedingly small: but although the maximum of effect can in fact be
produced only when these conditions are actually fulfilled, a gentle fall of the
current or water, and a sufficient velocity of the wheel may nevertheless be ad-
mitted without reducing the effect of the wheel materially below its maximum
of effect.
The author assumes for the purpose of an explanatory example a wheel of
11 feet in diameter, which he places in such a raanner that the surface of the
reservoir shall be situated at 12 feet from its lowest point, and that the first
action of the water shall take place at the highest point of the circumference ;
and supposing the buckets to be allowed a velocity of 4: feet in each second of
time, the resulting effect will be to the maximum effect as 11 to 12. But if it
should be required to encrease the velocity to that of 6 feet in each second of
time, it will in that case be found that the maximum effect will be reduced
one-tenth.
»18
He observes that it is thus shewn that bucket wheels do practically produce
very nearly a maximum efFect, whereas vertical wheels of the usual construction
produce at most but three-eighths of the maximum efFect; and that the two classes
of horizontal wheels produce one of them somewhat more, the other a little
less than half the maximum efFect.
It is observed finally by M. Borda, that the practical application of the different
sorts of hydraulie wheels here described, depending on a fall of water disposable
at pleasure, on the nature of the machinery to which they may be required to
be applied, and on many other local circumstances; no statement of general
advantages can be made in favour of any of them, but that from the general
principies he lays down in his memoir, a -correct comparison of their merits can
easily be made for any case which may occur.
(13. Piate 2.)
OF HORIZONTAL WIND-MILLS.
There is perhaps no machine more universally known than the wind-mill; or at
the same time any machine of which the true theoretical principies are §o little
understood, and which aresubject to such various inconveniencies. The vanes of
fhis machine are turned by the direct impulsion ofthewind; but the power which
acts to produce this motion, is frequently less than that which tends to overtum
the machine. From this circumstance there results the necessity in construeting
the vanes, of making them of excessi ve dimensions: such enlarged dimension»
greatly encreases the quantity of friction, renders the working with high winds
both difficult and dangerous, and in the event of hurricane even exposes the
whole machine to destruction.
The size of the wings occasion a very considerable lateral resistance; and if
the obliquity be considered which it is necessary to give them in order to obtain
the maximum of efFect, it will be seen that on account of this considerable
surface of the wings, the .efFect of the mill is seldom what might be expected.
The necessity of constantly directing the wings to the wind is one of the19
greatest inconveniencies; as the wind is continually varying, its direction ia
seldom such as is required. It sometimes may be found even to shift suddenly
to the opposite point of the horizon: in such a case., the mill is in great
danger of being destroyed; besides this, the inconveniences of the capstern, and
the difficulty of working it with sufficient alertness involves much unprofitable
labour, and oceasions much loss of time.
In wind-mills of small size a set of vanes are sometimes used, which enable
the wings to direct themselves to the wind ; so that from whatever point it pro-
ceeds they immediately assume their proper situation. In England this is gene-
rally effected in large mills by a small set of vanes acting on a large horizontal
toothed-wheel by means of an endless screw; but large vanes of this description,
when applied to mills of small size, as well as small vanes, when applied to mills
of large size, present obstacles of too serious a nature in their construction on
the one hand, and of expence on the other, to meet with general adoption.
These circumstances have engaged the attention of mechanical men, who have
sought the means of some more advantageous use of the power of wiud, which
might enable a mill to direct itself constantly to the wind without the necessity
of any manual operation. One of the most remarkable of these is a Dutch
mill, m which is a horizontal wheel with moveable wings: a certain number
of these are constantly in the direction of the wind, while the others are entirely
exposed to its impulsion, and consequently force the wheel round till the power
ceases, or some other cause stops the motion of the wings.
Intbefigure I 3, let us imagine—lst. ThatC 1, C2, C3, C4, C5, represent
a wheel eomposed of six frames set upon the spindle C. 2nd. That e k, d y, b i,
ah, gm, and f 1, are small vanes fixed to the same frame by theijrpivots d', and
that they are placed in such a manner that the vanes are divided into two unequal
parts by their axis of rotation.
Let there be placed in each fmme a check or stop as r r, &c. formed by vertieal
ropes at such a distance from the center as that the distance between the check
and the pivot of the vane, which belongs to that frame, shall be a little less than
the length of the kmger arm of that vane. The vane wiH consequently be at
liberty to tum freely on its pivot, without however being allowed to pass beyond
d 220
the direction of the supporting frame: which may be easily effectedby introducing
other checks, such as other ropes placed between those last mentioned and the
point of rotation.
It will be easily perceived that in whatever position the small vanes may be
during a calm, the moment the wind begins to blow, in whatever direction, the
vanes will of themselves assume their pvoper direction, by causing the spindle C,
to turn constantly the same way: this is a circumstance of great importance, and
would certainly have given this description of wings a decided advantage over,
vertical wings, if serious inconveniencies incident to them had not materially
lessened their value. That which we consider as the most important, is the con-
siderable resistance which takes place between the wind and that portion of the
wheel which places itself opposite to its direction. The continual shocks pro-
duced by the striking of the vanes against the check ropes, also diminish
the general effect of the machine, and tend to its destruction.
It has been unsuccessfully attempted to diminish these consequences by en-
creasing the number of vanes upon the same frame; but daily experience shews
us, that the general inconveniences. attending horizontal wind-mills overbalance
their advantages.
(K 3.)
OF WIND-MILLS WITH VERTICAL SAIL8.
These mills are composed lst of a moveable axis B, inclined to the horizon?
from 8 to 15 degrees. 2nd. Of four bars or arms of wood B C, B D, BE, BF,
each of about 37 feet in length, which are set at right angles to the axis B;
near its highest extremity. And 3rd, of four wings, which are supported by the
last mentioned pieces.
The wings are each 31 feet in length, by a little more than 6 feet in breadth ;
and extend from 6 feet above the axis B, to the extremity ofthe bar.
According to Messrs. Monge and Hatchett each wing maybe*considered to be
a bent or waved surface, generated by the motion of a right line perpendicular
to the piece which supports the wing. At the extremity nearest to the axis B, tha21
■wing makes an angle of 60 degrees with it on the windward side. The gene-
rating line traverses with an uniform motion the whole length of the piece which
supports the wing, always remaining perpendicular to it, but uniformly encreasing
the angle which it makes with the axis B, until arrived at the extremity of the
wing. It forms an angle of 78 degrees with it, if the axis B is inclined 8 degrees,
or of 84 degrees if the axis B is inclined 15 degrees; and in proportion for any
intermediate inclinatiom
The several positions of the generating line spoken of, will give the positio»
of each cross-piece of the frame which receives the sail of the wing.
Each wing may thus be considered a waved surface, generated by the motionr
of a right line perpendicular to the supporting piece, and coinciding in every
part of its progress with a right line drawn between the corresponding extre-
mities of the generating line at the'two extremities of the wing as already
described.
The dimensions here given are those which are generally adopted in Planders,
in the neighbourhood of Lisle ; and are described by M. Coulomb, in a memoir
of the Academy of Sciences for 1781, to which we refer the reader.
In calculating the total effect of these mills, lie estimates that they will raise
lOOOlbs. weight 218 feetineach minute of time, working. constantly at the rate
of eight hours each day.
M. Coulomb observes with M. Bemouilli—supposing a man to use his power
in the most advantageous manner, and to work eight hours per day, he will not
be able to raise more than 60 lbs. weight in each second of time : which, pro-
ducing 1,728,000lbs. weight raised to the height of 1 foot, for the daily effect,
we shall have upon the calculation of 8 hours’ labour in each day, a total weight
of l,0001bs. raised to- the height of three feet and six-tenths in each minute ; and
as we determine that the mill in question working at the rate of 8 hours per
day, will raise 1000 lbs. weight to the height of 218 feet in each minute, its
whole effect will equat that of the daily labour of sixty-one men-.
In the memoirs of the Academy of Berlin for the year 1756, we find a memoir
of M. Euler on the theory of wind-mills : in which he determines that the wing
should form an angle of 54 degrees 44 minutes, with the supporting shaft atthat point of the wing immediately contiguous to it, that at its ex tremi ty it
should form with the shaft an angle of 80 degrees; and that the velocity of the
extreme point of the sail should be somewhat more than twice that of the wind.
A memoir of M. Lambert, in the memoirs of the Academy of Sciences of
Berlin for the year 1775, may be advantageously consulted on this subject.
The dimensions of the wings of wind-mills, their form, the methods of adjusting
them to the direction of the prevailing wind, the means afforded of spreading,
and of taking in the sails, are likewise considerations which have constantly
engaged the attention of mechanicians and men of Science.
The following works may also be beneficially consulted:
Leupold Theatrum Machinarum.
Description de 1’art de construire les moulins, by Beyer; enlarged by Wein-
hold. Dresden, 1788, in folio.
Dessins artificiaux des toutes sortes des moulins avent, &c. by Jean de Strada
de Rosbery. Published by Octave de Strada, Frankfort, 1617, and 1629, in
folio.
Theatrum machinarum novum, &c. by Gregorium Andream Bocklerum, 1662.
This work also contains the greater part of the machines described in Strada’s
work. Bo,ckler also published a work in folio, under the title of " Architectura
curiosa nova,” which contains a collection of such fountains as are remarkable
by the variety of their arrangement and effect.
Schapp’s work, entitled “ Theatre des Moulinsthe mechanical portion of
the first part, with five supplements. Frankfort, 1766, in quarto.
There are few coilections of machines which do not contain accounts of various
constructions of wind-mills *.
A description of two mills, which deserve some attention, will also be found
in the Annales des Arts et Manufactures, Nos. 20 and 41.
* As for example—in the u Collection des machines approuvees par 1’ Academie^” in toI* i. pages 105
and 107; and in yol. yii, page 117.23
(L 3.)
A description of a steam engine with a direct motion was contributed to the
account of productions of the national industry, by M. Verzy in the year 1806,
and which we shall now describe :—
Let abcd be thesection of a cylinder taken at right angles to its axis, and let
the heiglit of the cylinder be equal to the distance m n, -which is the space that
separates the cylinder abcd from a second cylinder efghie, situated concentri-
cally wifthin the first; so that the two cylinders ha ve one common axis, and the
surfaee of the second is accurately adjusted to the upper and lower edgesof the
first or outer cylinder.
Between the two cylinders there is thus a sort of circular channel, the horizontal
section of which is represented in-the figure by kebfhlmnke, and the heiglit
equal to the piate m n, which is attached to the outer cylinder and breaks the
continuity of the circular channel already mentioned: the ends of the interior
cylinder are closed by plates of metal, which form a stnall border or ledge on the
upper edges of the exterior cylinder. They are attached to the axis C, solthat
the interior cylinder xnay be at liberty to turn freely about. on its axis, supposing
the exterior cylinder to remain fixed.
In the curved surfaee of the .interior cylinder are made two apertures e i, gh,
diametrically opposite to each other; and in width and height equal to the circular
channel or passage already spoken of. -Two shutters or valves of an angular
form k e i, ghl, are provided, which tum on tbeir axes e and h, andact so as to
close the apertures ei and gb, and also the circular passage at the sarae time by
means of two spiral springs epq, hrs, fixed on the upper extremities of their
axes, and the elasticity or force of which may be encreased or diminished at
pleasure. These axes project above the upper face of the cylinder, and have
each a lever handle which respectively project from the axis in the directions
ek, hl.
The curved surfaee of the exterior cylinder is perforated by two circular aper-
tores, one which tertninates the tube A, which conveys steam to the cylinder,
and the other communicating with the condenser by means of the tube B.
This being clearly understood, if we imagine that steam enters the cylinder by24
tlie tube A, the piate mn obstructs its passage, wliilst the two sides or arms ke, ei,
of the angular valve presents the sarae quantity of surface, and consequently the
valve will not alter its position ; but its edge will press ori tlrat of the interior
cylinder with the whole force of the spring epq, and that cyliuder will revolve
about the common axis of the two cylinders, and in the direction ab c. Before k e
arrives at the aperture B, which comraunicates with the injection pipe, the lever
handleat h, will have encountered the obstacleor checkat o, which isasmallbar
or pin fixed to the outer cover of the exterior cylinder, and will have forced the an-
gular valve g h 1 within to tum inwrards: thus passing the fixed piate m n, so that
when it re-assumes its first position, k p will have passed the aperture B, and
the vacuum will be formed in the portion keblrfp of the passage, and every
thing will be in the situation represented in the figure. The interior cylinder
will only have made a half revolution ; the action of the steam will continue to
communicate a continued rotatory motion to the axis, wrhich may be applied to
any use at pleasure.
Various machines on this plan have been constructed in England for a con-
siderable time. Descriptions of such may be seen in the Repertory of Arts and
Manufactures.
(M 3.)
PLAN AND ELEVATION»
The intended effect of this machine is to produce the immediate conversion of
the rectilinear motion of the wind into circular motion. It is an universal wind-
mill, but is not so practically useful as it is curious.
(N 3. Piate 10.)
THE MACHINE OF THE MARQUIS MANNOURY D*ECT0T.
The piate consists of an elevation, an horizontal section in the line cc1 of the
elevation (marked a in the piate); and a second horizontal section in the line d'd
of the elevation (marked b in the piate).
It is well observed by M. Petit, that this machine may be classed among
hydraulic wheels :—it consists of a cylindric wooden tub ncdd'crn, thebottom
*>f which has a circular perforation rr in the centre, as represented in the25
elevation and the section b. Through this aperture there passes an iron spindie
pq, which is held at its upper extremity by a collar, and has its lower extremity
resting on a pivot, which allows it a rotatory motion on its axis, and carrying
the tub with it in its motion, by being attached to it by cross bars of iron, two
of which cc' and e e' are shewn in the section a, and the other two dd7, ff7 in the
section b. The spindie, which lies in the direction of the axis of the tub, does
not completely occupy the circular aperture which it passes through, but leaves
around it an open annular space through which the flowing water has liberty
to escape. A circular diaphragm ss, fixed to the vertical axis pq, and also to
the cross bar cc' e e' immediately below them, serves to divide the tub into two
equal portions in the direction of its depth, as n c c7 n and c d d7 c. These divisions
or compartments of the tub, c d d' c, have no means of communication except
by the annular space which remains betvveen the edge of the diaphragm and the
inner surface of the tub. The lower portion or compartment of the tub c d d7 c7,
is divided into eight smaller compartments by so many divisions t, four of these
proeeed immediately from the axis towards the circumference: the other four do
notextend so far as the axis, in order not to cause too much obstruction tothe
opening r r. These diaphragms are composed of flat surfaces, and continue from the
circular diaphragm to the lower partof the tub. Water is made toenter at the upper
part of the tub by a conduit-pipe B, which is bent in a suitable manner so as
to allow it to flow out by an aperture x shewn in the elevation, and in the
section a. It flows in a sheet which strikes perpendicularly against the concave
surface of that part of the tub, setting the tub in motion, and descendi ng to its
lower compartment by the annular space provided between the diaphragms ss,
and the inner surface of the vessel, penetrates the eight divisions already spoken
of, and finally quits the vessel by the aperture rr, and falis into the discharging
pipe R.
This is the description and mode of operation of this machine, which the
inventor has adopted mvarious different instances with perfect success. He has
recently added an improvement which consists in substituting for the flat dia-
phragms t, curvcd or spiral diaphragms, which extend upwards as far as the
upper edge n n of the tub, through the open space in the middlie. The figure
E86
of these improved diaphragms enables him to dispense with theflanch nn, and
which prevented the water from escaping in that directkm: it appears that by
this improvemeut the loss of momentum is considerably diminished.
O 3. Piate 10.
M. CAGNIARD LATOUR’s MACH1NE.
This machine is composed of two tubs or vessels A and B, the firs*t filled with
water at the ordinary temperature, the second filled with hot water the temper-
ature of which is of at least 75 degrees of the centigrade thermometer. In
the first tub is placed an Archimedean screw C, and in the second a water wheel Dj
a tube ab ede f, communicates from the bottom of the first tube to that of the
second.
If the Archimedean screw be turned in a direction contrary to that in which it
would be necessary to turn it, in order to raise the water contained in the tub, it
will cause atmospheric air to descend by its spiral passage; and this, after passing
through the tube of communication abed e f, will be delivered at its aperture f.
It is hardly necessary to premise that the distance of the aperture f from the
surface of the tube B, shonld be somewhat less than that of the aperture a, from
the surface of the vessel A. The cold atmospheric air, carried in this manner to
the bottom of the tub filled with hot water, will under those circumstances,
become dilated with the encreased temperature, enter the compartments of the
wheel by the open or outer ends, which are turned downwards, and so cause the
wheel D to revolve.
M. Camot, in a report made to the Institute, May 8th 1809, upon thismachine,
observes thus:—In the machine exeeuted by M. Cagniard, the effect pro-
duced is to raise by means of a rope attached to the shaft of the wheel a weight
of 151bs. with an uniform velocity of one inch in each second of time, and in
a vertical direction; whilst the moving power applied to the screw is only three
pounds weight with the same velocity: so that the effect of the encreased tem-
perature seems to be that of encreasing the natural effect of the moving power
five-fold.27
We may conceive that the effect of the moving power being encreased five-
fold, we may deduct from that effect and add somewhat to the moving power;
and stili find that we retain a disposeable power of four times the original or
moving power, which is what has been effected in M. Cagniard’s machine, as will
be seen by the figure.
This application of the Archimedean screw produces one of the best arrange-
ments for blowing engines. At Clichy we find it adopted in a manufactory of
whitelead in which the screw is of the dimensions of four feet iri diameter, and
five feet in length.
(P 3. Piate 10.)
The appellation of Crab, is given to a machine composed of an horizontal
roller, which is used to lift heavy weights, either by means of a simple pulley, or
sometimes with the additional help of combined pullies of different powers; these
machines afford a general solution of the problem proposed to be resolved in
this section.
We have in this instance a machine of this description, in which the required
effect as to the relative velocities isnot produced by the use of a compound pulley,
but by substituting for the ordinary cylindrieal roller, a roller which eonsists of
two cylindrieal portions of different diameters, and on one common axis: see A
E in the figure. A rope A B C D E, after making several turns on the portion A
of the roller, passes over the simple fixed pulley B, and thenee to the simple
moveable pulley D, to which is attached the weight P; it then returas, and pas-
sing by a second fixed pulley C, goes finally to the other and smaller portion E
of the roller A E, on which itis wound up in a contrary direction to that in which
it was wound on the first portion A; so thatwhen the cylinder is made to revolve
on its axis, the rope is wound up, or gathered upon the portion A of the roller,
while it is unwound or released from the portion E. The moving power is applied
to the extremities of the levers 11. It will be easily conceivcd that at each rotation
of the roller A E, the weight P will move through a space equal only to half the
E 228
difference of the circumferences of the two portions A and E of the roller; and
it will also be evident that the difference may be made small at pleasure.
The description of a double capstem*produced by an application of this prin-
ciple will be found in vol. xix, page 305 of Les Annales des Arts et Manufactures.
SECTION 1Y.
To convert a given direct and equable rectilinear motion, or the velocily of which
varies by a given law, into alternate circular motion of velocity simitar to
that of the moving power, either equable or variable by a given law; and in the
same, or in different directione.
(A 4.)
IP direct rectilinear motion be converted into direct circular motion by any
of the arrangements pointed out in Section 3rd, ali the examples shewn in
Section 9 will apply to this section.
(B 4.)
It has been proposed by M. Perrault, of the Royal Academy of Sciences
(Recueil des Machines approuvees par 1’Academie des Sciences, Vol. i. Nos. 9
and 10,) to apply the fall of water as a mover for a pendulum clock. Without
pledging ourjudgement as to the usefulness or merit of his machine, we shall
explain the organization he has adopted for converting the rectilinear direction
of the moving power into an alternate circular motion.
Water is made to fall, as at c in the figure, into the vessel d, which is constructed
to tum or swing on an axis m, and is divided in the middle into two equal parts
by a partition. When the base of this vessel is in an horizontal position, the
water falis so as to divide itself equally by the partition before mentioned, and in
any inclined position the whole quantity of falling water will be received by that
side of the vessel which is elevated. In the position shewn by the figure, this entire
quantity is received by the side b of the vessel; when that side of the vessel becomes
full, it turns on its axis in the direction of that side, and descends till it reaches
and rests on the stop or support f, pouring out, by this change of position, the29
quantity of water which produced the motion. The opposite side filis in it»
tum, and bri »gs the vessel into its first position, resti ng on the support g ; and
the operation is repeated.
.. (C4.)
Problem.—To convert alternate circular motion into direct rectilinear motion.
Let AB of tliisfigure be aleverturning about on an axis C, and FG an upright
bar, which is at liberty to rise and fall -easily; and having a strait ratehet on
eacli of its longitudinal edges. DE, D E are two small levers turning on pivots
at D and D, and have their other extremities E E, turned so as to engage in
the teeth of the ratehet already mentioned. The alternate circular motion of
the lever A B will operate to raise the bar FG. M. Perrault, of the Royal
Academy of Sciences, has applied a piece of mechanism of much similitude to
tliis, to the construction of an engine for raising heavy weights. It will be
found in the Recueil des Machines approuvees par 1’Academie, Vol. i. No. 1.
(D 4.)
A boat at anchor in the iniddle of a river, if heid by a cable of sufficient
length, will move alternately from one bank of the river to the other, by means
ofits rudder; furnishing an instance of alternate circular motion from direct
rectilinear: this is a well known contrivance, and is of frequent application.
(E 4.)
A sector of a circle surmounted with a sail, forming together a combination,
the centre of gravity of which shall be situated considerably below the centre of
i oscillation, by means of the application of a counterpoising weight, will swing
to and fro continually, with an alternate circular motion produced from the im-
pulsion of the wind upon the sail: this mode of applying the direct action of the
wind has been often proposed, and many models constructed on this principle
may be found in the Conservatory of Machines of Paris; and in the work of
M. Alexander Bailey, which includes the description of machines presented30
to the Society for the Encouragement of Arts and Manufactures of London: the
applicatiori of this contrivance as a first mover to an hydraulic machine by
M. Merryman, will be found in vol. i. page 154.
All machines which are applied to the purposes of raising water by means of
an oscillatory or alternate circular motion, communicated to the machine by
any power whatever, and which is applied to them exteriorily, as are those for
instance which are described in the Journal des Mines, No. 66, may be placed
in this fourth class.
The Bulletin de la Societe d’Encouragement, for August, 1811, No. 86,
contains a description of a machine termed an Hydraulic Pendulum, by its in-
ventor M. Boitias. M. Molard, in a report upon this machine, made by him to
the Society in December 1808, and which is contained in the 54th Number of
the work above mentioned, makes the following observation:—“ With respect
to the hydraulic pendulum, this machine must not be eonfounded with a contri-
vance under the same name, described by Belidor, for the purpose of raising
water. It is a simple pendulum which receives its oscillatory movement by
means of the current of a river, and with the additional aid of a counterpoising
weight.
To produce this effect, the author has placed a float board of considerablesize,
and mounted on asupporting pivot,at the lower extremity of the pendulum; it al-
ternately assumes the verticaland horizontal position. In the first itdipsinto the
current and obeys its pressure ; in the second it obeys the effect of the counter-
poising weight, which bring's it back to the position from which it set out, in
order to coinmence another oscillation,’*3i
SECTION V.
To convert a given direct and equable rectilinear motion, or the velocity of whick
varies by a given Une, inio a direct curvlinear motion of velocity similar to
that ofthe moving power, either equable, or variable by a given lato, and in
the same, or in different directione.
DIRECT rectilinear motion may be converted into direct circular motion
by the methods exbibited in Section III.; and the arrangements shewn in
Section X. will afFord examples of the required conversion.
SECTION VI.
To convert a given direct, and equable rectilinear motion, or the velocity of whick
varies by a given law, into an alternate curvlinear motion, of velocity similar
to that of the moving power, either equable or variable by a given law, and in
the same, or in different directions.
DIRECT rectilinear motions may be converted into direct circular motions
by any of the arrangements exhibited in Section III.; and then the examples of
Section II. will afford instances of the required conversion.
SECTION VII.
To convert direct circular and equable circular motion, or the velocity of whick
varies by a given law, into alternate rectilinear motion of velocity similar to that
of the moving power either equable, or variable by a given law, and in the same,
or in different directions.
(A 7.)
LET ABDE, piate 2, be a wheel which is at liberty to revolve on its axis
in the direction indicated by the letters ABDE with an uniform velocity;32
mn is an index which is obliged to observe the same direction, while the extre-
mity m follows the figure of a curve drawn on the surface of the wheel; the
other extremity n, is also required to make a determined number ofback and
forward motions of given extent; and returning with each revolution of the
wheel to the same point froin which the rnotion commenced, and this with a
velocity either uniform, or which varies by a given law, or which is even en-
ti rely arbitrary.
If the ratio of the velocities be uniform, or if they foliow given laws, the curves
which will be thus described will be determinate and easy of construction. On
this subject a memoir of M. Deparcieux may be consulted on the mechanical
methods of describing those curves which occur in the construction of machines
intended to move levers or balance wheels. It is printed in the memoirs of the
Roval Academy of Sciences for 1747.
If the ratio of the velocities be arbitrary, a solution of the problem may be
afforded by a great variety of curves; and by rectilinear polygons as well as by
curved. Rectilinear polygons afford angles too acute—curvlinear ones are
therefore to be preferred.
The applicatiori of this problem is of considerable use in the art of turning.
(B 7.)
This is a particular case of the subject of the last problem, in which at each
revolution of the wheel we obtain but a single alternate stroke, aud that an
uniform motion. The curve being proportional and all its diameters equal, that
circumstance is rendered advantageously available by subjecting the motion of
the rule or bar ab, to the curve, by means of two metal pins n m, which are
fitted with friction rollers, against which the curve acts through its whole course.
The pieces which carry the threads in the bobbinsof the silk-throwing machine
of M. Vaucanson, are put in motion by an application of this curve. It is also
used in different hydraulic engines to afford an uniform motion to the pistons
of pumps.
In the 23rd number of Les Annales des Arts et Manufactures, we find the
description of a new spinning-wheel by Mr. Antis, an Englishman, for which33
the Society for the Encouragement of Arts, &c. of London awarded a premium
to that gentleman.
C 7. Plan and Elevation.
Let A B C in the plan of the figure represent a piate of metal, through the
thickness of which are cut the grooves or channels ab, cd, &c.: behind the
piate ABC, and close to it, let us suppose a second piate NM (shewn in the
elevation or upper figure); in this piate is cut, also through its thickness, the
spiral channel indicated in the plan of the figure by the double dotted line, and
described on the same principies as the curve of the preceding figure B 7 : it is
evident that if the small cylindrical pins r s pass through the intersections which
the spiral will form witli the channels ab, cd, &c. and the hinder piate be made
to move, ali the cylindrical pins will approach to, or recede from the centre by
an equal distance. Now if the bent arms sn be added to those cylindrical
pins forming radii to the circle, and their lengths be such that their extremities n
shall terminate in the circumference of a circle concentric to the piate; it is
evident that these extremities n of the arms, will in every position, whether ad-
vancing to, or receding from the centre, also be situated in the circumference of a
circle concentric to the same circle. Two pieces of mechanism similar to this
may be arranged one over the other, as is shewn in the elevation of the figure;
and the extremities n of the bent arms may be connected so as to compose a kind
of cylinder whose diameter may be encreased or diminished at pleasure by the
rotatory motion of the spiral plates before described. This ingenious arrange-
ment is adopted in England, in the construction of lathes, and in other machines
in which it is occasionally required to alter the relation w'hich the moving power
bears to the resistance, and where itis necessary to effect this with quickness and
facility. Other applications of this contrivance may be found in the Repertory
of Arts and Manufactures, vol. xvii.; which contains the specification of a patent
obtained by R. Brayshay—for a machine for the purpose of gaining an increased
speed and power to ali mechanical operation by land and water :” dated Oc-
tober 30th 1801; and No. lxxi of Les Annales des Arts, &c. by R 0’Reilly.
F
f(D 7.)
The whcel A B (of which the figure shews a side elevation) has its periphery
formed into teeth of any figure at pleasure: the arm a b is made to press eon-
stantly npon the teetli of the wheel by means either of a spring or the application
of a weight, and is at liberty to slide through the pieces c and d, while it pre-
serves its perpendicular position with the plane of the wheel. If the wheel be
turned, it will communicate to the arm ab, an alternate rectilinear motion,.which
may be varied to suit the required purpose. It will not be difficult to determine
the figure of the teeth upon the principies spoken of under the article (A 7).
A very ingenious application of this motion has been made by M. Zureda in
his carding machine. The same motion has also been latterly applied to a
machine for the manufacture of fishing lines.
Leupold, in his work “ Theatrum Machinarum Hydraulicarum, vol. ii. p. 36.
fig. 3, shews an application of this contrivance to a motion for pump pistons.
The vertical axis of an horizontal hydraulic wheel carries another horizontal
wheel, on the upper side of which are arranged seven inelined planes, forming a
kind of ratchet wheel, having the spaces or intervals between the teeth nearly
equal to the base of the inelined planes which compose the Avheel; the piston
rods of the pump are fitted with projecting pieces which rest on the wheel by
friction rollers; so that at each revolution of the first wheel or mover, the pump
pistons make seven ascending, and seven descending strokes, or seven alternate
rectilinear motions.
(E 7.)
The circle A of this figure has a motion on its axis, and a projecting point or
pin fixed on its face passes through the groove n m of the lever P Q, whose
centre of motion is at R. It will resuit from this arrangement that the direct
and uniform circular motion of the wheel A will be converted into an alternate
circular motion ; and the two extremities of the lever P Q will traverse with un-
equal velocities, and the machine will belong to the class of the ninth section.
But if a portion of a toothed wheel be set on the extremity P of the lever which35
shall act in the rack-bar N M, an alternate reetilinear motion of unequal ve-
Tocity will be obtained, and which will belong to the arrangement of Section VII.
By means of the simple fixed pulley G, and the rope QGH fixed at Q and
sustainina: the weigrht H we also obtain an alternate reetilinear motion of un-
equal velocity.
Another alternate reetilinear motion of unequal velocity will also be obtained
by placing a pin or small cylinder at the intersection of the groove p q of the
lever P Q, with a groove s t described in the fixed bar X y, the cylinder so
placed will have the required motion.
Les Annales des Arts et Manufactures, vol. xv, page 119, contains an ap-
plication of this motion to an improved machine for cutting the teeth of
wheels.
(F 7.)
PLAN AND ELEVATION.
A is a wheel of which a portion only is toothed, and which turns eonstantly
in the same direction on a fixed centre; B C is a chase frame, the two inner
and opposite sides of which are formed into racks. To the ends of this frame are
firmly attached the bars B S C T, which are at liberty to move to and fro within
the clips p q, n m; the frame with its two bars, which may thus be considered
as one piece, thus acquire an alternate reetilinear motion by conversion, from
the direct circular motion of the wheel A. The frame which contains the two
racks might also be applied to a bar, by a simple change of construction.
If the teeth of the wheel were infinitely small, they ought to occupy one half
of its periphery and the remainder be left plain. The length of the two racks
will be equal to half the periphery of the moving wheel, and their extremities
will be at equal distances from the short sides or ends of the frame: but when the
teeth of the wheel are of larger size, which must always be the case in practice,
the toothed portiotl of the wheel must be less than half its periphery; the racks
will be equal in length to the toothed portion of the wheel, and they will termi-
nate at unequal distances frm the ends of the frame. The number of teeth for
the wheel is arbitrary, but great mechanieal precision is required in the practical
exeeution of this machine.
p 236
The teeth of tlie wheel and of the racks will be described with sufficient faci-
lity by reference to the instructions for that process given by M. Camus, in the
second volume of his “ Course de Mathematiques” *.
When the portion of the wheel to be formed into teeth is determined on, and
thence the lengtli of the rack, and the situation of one of them, that situation of
the other which shull afford the maximum effect in the entire machine may be
easily determined by trial: the theoretical discussion would lead us from our view
of the subject without affording adequate advantage.
Applications of this motion to the alternations of pump pistons may be found
in the description of M. Augur’s pumps, (Machines approuvees par 1’Academie
des Sciences de Paris., Vol. iv, No. 223).
Examples of the conversion of a direct circular motion, into an alternate rec-
tilinear motion, by means of a wheel of which only a part is indented, and one
or two racks; and also of the conversion of direct circular into alternate circular
motion, may be found in the Repcrtory of Arts and Manufactures, London,
Vol.xii. page 145; in Berthelot’s work—Mecanique appliquee aux Arts, aux
manufactures, a l’agriculture, a la guerre, vol. i. page 59; Moulin a pedale vol. ii.
page 36; Machine a manege pour scier la pierre, vol. ii, page 40; Scie a de-
bater le bois.
In the Ist volume ofa work by J. Leupold, printed at Leipsic in 1724, entitled
Theatrum Machinarum generale, chap. 12, the author undertakes to shew five
different methods of converting direct circular motion into alternate rectilinear.
The first of these methods which he shevvs in piate 25, figure 1 of his work, cor-
responds with our arrangement (F 7). This second method, piate 25, figure 2,
is actually the same: the only observable difference is that the bar represented by
TS in our figure' (F 7) is vertical, and that the two racks instead of being toothed,
are formed of a series of small horizontal cylinders similar to those which are
used as trundles in the lanterns of mill-work; the motion ofthe bar TS is applied
* Further Information on the subject may likewise be found in “ L’Essai sur 1’Horlogerie,” by F. Ber-
thoud, Paris 1786, vol. ii, page 13; the 4th volume of the French Encyclopedie, article u Dent” ; and
the Disserta tions of M. de ia Lande, in u Le Traite d’Horlogene de M. Le Paute.37
to the piston of a pump: this application had already been made by R amelli.
The third method (figure 3, piate 25), does not materially differ frorn the pre-
cedi’ig; it is in substance a lantern pinion, which is partly fitted with trundles,
instead of a wheel partly indented, and the teeth of the rack are rounded. The
fourth method (fig. 4) is composed of two vertical racks, having their flat sides
placed parallel to each other, and their racked edgeslying in the same direction.
The upper extremities of these racks are attached to the ends of a rope which
passes over a simple fixed pulley; the racks being thus suspended, it follows
that whenever one of them is made to ascend, the other will descend by its own
weight; an horizontal spindle is placed across the front. edges of the racks, and
two lantern pinions partially fitted with trundles are set on it so as to act on
the racks; their positions are so adjusted in the first instance, that when the
trundles of one of them act on the corresponding rack and cause it to ascend,
the blank space of the other pinion is opposite to the other rack, which is there-
fore at liberty to descend. The author applies this mechanism to the movement
of pump pistons in his work entitled, “ Theatros des Machines Hydrauliques,”
printed in 1724, vol. 2, piate 40, fig. 8. In his fifth and last method, the author
converts the direct circular motion into alternate circular, by our arrange-
ment R 9, piate 7, in which B and C are two pinions, and A a wheel partly in-
dented. Ile again converts the alternate circular motion of the bar d e of our
figure, into an alternate circular motion by our arrangement (D 8), piate 5 : for
this purpose he places an endless screw on the horizontal bar d e, which works
in the segment of a wheel; the extremities of the segment are continued hori-
•zontally, and carry the piston rods of two pumps. The description we have
here given will shew that the five supposed methods of the author are reduced
to one, the arrangement' of which admits of but little modification.
By laying aside one of the two racks, and introducing an entire toothed wheel,
the alternate circular motion may be converted into an alternate rectilinear
motion. as will be stmwn in our figure (M 17). This arrangement had long been
applied in the process of coining—for milling the edges of the pieces under
operation, but its use has since been discontinued.
A very simple and ingenious method of avoiding the loss of time which would38
take place In this piece of mechanism at each cliange of direction of its motion,
was invented by M. Doinet. An additional tooth inavked a, in the figure (F 7)
is set on the wheel A, but below the level of the other teeth of that wheel. An
additional tooth is also set on each rack, and in the sanie plane or level with
the additional tooth of the wheel. The action of the tooth a, npon the additional
teeth of the racks operates to continue the motion of the bar T S duririg the in-
terval which elapses between the action of the wheel ceasing on one rack, and
iis commencement on the other.
In Bockler’s work, already raentioned in speaking of our fi gure (E 3,) we find
lhe direct circular motion of a vertical spindle converted into an horizontal and
alternate rectilinear motion by the arrangement we have described in our account
of F 7. A vertical spindle carries an horizontal lantern pinion, the trundles of
which work into two rows of pins arranged upon the inner edges of a frame,
which is thus substituted for the racked frame of our figure. In Bockler’s
machine it may be observed by figure 71, that each rack is terminated at the
opposite ends by a pin somewhat longer than the rest: this is evidently intended
to correct the loss of time incidental to the changes of direction. The author
then converts the horizontal alternate circular motion into the vertical and alter-
nate rectilinear motion, required for working pump pistons, by an intermediate
alternate circular motion, which he effects by a contrivance similar to our figure
N 7, piate 3 : thus—To the end of the piston rod he fixes a bar which extends
to the edge of a cylinder or horizontal circle, whose axis is perpendicular to the
vertical plane passing through the piston rod, and the spindle of the frame;
another bar is placed from one end of the frame to a point upon the edge of the
cylinder 90 degrees distant from the attaching point of the bar first mentioned.
Th ese bars tum frecly at their ends, as the bar n rn in* our figure N 7. This
mechanism resembles that in convmon use in bell-hanging, for transferring alter-
nate rectilinear motion from one apartment to another. He also shows other
applications of the same arrangement.
G 7. Plan and Elevation. Piate 3.
Iu this arrangement the frame containing the racks is made somewhat large?39
than that of the preeeding article, by having the racks themselves longer, so as
to meet at the ends, where they continue in a semicircular form, and the small
wheel or pinion is completely toothed. It has been found necessary to allow a
small lateral motion to the rack-frame, which is given at the end of each alter-
nation by means of two cross pieces a b, c d, in order to facilitate the change of
direction of the rack. In general however, this motion involves considerable
difficulty in the practical execution; and it appears but little adapted to produce
any important effect.
In a report made by Messrs. Prony and Mollard, upon the methods proposed
to replace the hydraulic machine of Marly, we find a machine projected by
M. White, in which this motion is introduced.
In Bockler’s work—Theatrum Machinarum novum, &c. the same mechanism
is applied to convert the direct circular motion of an horizontal spindle into an
alternate and vertical rectilinear motion for pump pistons : Bockler’s contrivance
for equalizing the motion of the vack-frame does not appear of sufficient merit to
recommend it to notice; but in the course of this work we shall introduce a
variety of methods for that purpose,
H 7. Plan and Elevatiom
This is a modification of the motion shewn in F 7. In this machine the number
of teeth in each rack is reduced to one, and those of the wheel are entirely super-
seded ; they are replaced by projecting amis, each having a small friction roller
at its outer extremity. It will be readily observed that this strait fi gure of the
teeth of the racks will occasion an irregularity in the rate of their alternate
movements ; but the law of this velocity may either be varied at pleasure, or
rendered uniform. by making the teeth of a suitable figure.
The construction of this machine is to be preferred to that of F 7 : for all ar-
rangemeuts which are exposed to violent action, and to which small teeth of the
usnal form and dimensions would not offer sufficient resistance. The eng-ine in
this form will be los» costly in its original construction, and will be made with
greater facility: incidental repairs will also be more easily made.40
In the first volume of cc Machines approuvees par 1'Academie des Sciences’’,
we find tliis movement applied to the construction of a machine for sawing
stone, &c.; and anolher appiication of it in the “ Traite de la Gravare a l’eau
forte” of the old Eucyclopedia.
1 7-
In this figure A represents a wheei which turns on its axis; n and m two clips
between which slides the bar P Q, with the attached cross-bar RS; s is a pivot
which is allowed to pass through the groove pq. The circular motion of
the wheei A will under this arrangement produce an alternate motion to the
bar P Q.
This alternate rectilinear motion is very slovv at its eommencement, but is
accelerated as it approaclies the middle of each alternation: it is evidently ex-
tremely simple and easy of construction. This is also a modification of the ar-
rangement shewn at P 7.
In the first volume of " Machines approuvees par l’Academie des Sciences”,
this contrivance is applied to the construction of a machine for sawing marble.
It is uscd in the ribbon weaving machine, to give the stroke for throwing the
shuttle; and is also sometimes used in domestic economy, in a machine for
churning.
In the eighth volume of the Repertory of Arts and Manufactures, we find thi9
movement adopted by Air. Bunting, in his calendering engine. His first mover
is a horse, which is applied to tura a vertical spindle ; at the upper extremity of
this is a pinion which drives an horizontal wheei. The direct circular motion
of this wheei is converted into an alternate rectilinear motion by the means al-
ready described ; the height of the arm which receives this motion being inconve-
nient, the author transfers his alternate rectilinear motion to another arm lying
in a parallel direction to the first, and at the required height, by meaus of an
intermediate alternate circular motion E 17. The polisher of his machine is
fixed to this second arm.
(K 7.)
The alternate rectilinear motion of the bar P QRS, figure 17, may be readily
ecjualized by substituting a groove of the curve represented at pq in the figure,
for the strait groove pq, of the figure I 7.41
The method of describing this curve is very simple: the distance C s is
divided into a certain number of equal parts, as for example six, sl, 12, 23,
34, 45, 5 C ; and the quadrant s d is to be divided into a like number of
equal parts. It is evident that the conditions of the problem will be obtained
if that point of the bar PQ which corresponds with the point s of the figure
be made to coincide with the divisions 1, 2, 3, &c. of the radius s C, at the
same time that the pivot s itself shall coincide with the corresponding divisions
1, 2, 3, &c. of the arc sD ; it will be necessary therefore to determine the
position of the points 1, 2, 3, &c. of the curve p s q, so that each shall be
placed with relation to the point s, as the corresponding points of the arc s D,
are placed with relation to the points of the same name in the radius s C, which
will not be found difficult. The same process will be followed for each of the
three remaining quadrants of the circle.
L 7.
In this figure a b is a vertical bar, which slides between the two rings
n m; a pestle is fixed on its lower end b, on one side of the bar is fixed a
rack in which works the indented portion of the wheel A, the remaining part
of wrhich is without teeth. When the plain portion of the wheel is opposite
to the rack of the bar, the pestle P will fall by its own weight upon the
body M : but if the wheel be made to tum in the direction of the dart in
the figure, when the teeth arrive at the rack, and begin to act, the pestle
will be gradually elevated ; but will fall again when the plain portion of the
wheel again arrives at the rack, and this alternate motion will be continued
with the action of the wheel. This is another direct instance of the arrange-
ment F 7. It is in frequent use for machines for the purpose of bruising
and pounding hard substances.
If for the rack and bar were substituted a toothed wheel which should turn
in the same direction as the pinion A, either by a weight P, attached to a
rope, which should be wound on its axle, or by a spiral spring: the direct
circular motion of A would be converted into an alternate circular motion,
and the arrangement would be classed in Section 9.
This mechanism was applied to work the pistons of two pumps by De Caus,
642
an architect and engineer, and is described by hira, in a work entitled “A
new iuvention for raising water above the level of its source, by means of
certain hydraulic machines.” London, 1644.
The author caused a vertical wheel having half its periphery indented, to
tum by the immediate action of a moving power, and on the right and ieft
of this wheel he placed two others of equal diameter, and which he supposed
to be partially indented, but which might also be completely indented, ac-
cording to the construction described in our last article ; he communicated
each of the piston rods of the two pumps witli one of these wheels by means
of a rope attached to the end of the piston rod, and by its other extremity
winding about the cylinder or spindle of the wlieel; the rope was so wound
on the spindle that the piston acted by its weight to turn the wheel in the
direction which converted the direct circular motion of the moving power,
into the alternate circular motion of the lateral wheels ; and consequently the
pistons received their required alternate rectilinear motion ; one of them-
ascending while the other descended by the action of its own weight.
The author in order to facilitate the descent of the piston, caused a rope to
pass over a simple fixed pulley placed over the middle wheel, and after-
wards to wind itself about the axis of the two lateral wheels, and in the
same direction with the corresponding ropes of the piston rods ; so that
when one of the pistons was raised, a part-of the action of the moving
power was at the same time employed to assi st the descent of the other;
the wheel being turned in the proper direction, the piston had to overcome
a resistance at least equal to the inertia of the wheel, with its friction, and
the rigidityof the rope, and in short, a resistauce equal to the power required
to set the wheel in motion.
M 7.
This is a modification of the mechanism of the preceding article. The
teeth of the rack are reduced to a single one, and the wheel is fitted with
cams or curved projecting pieces, the curvature of which is such that the
resistance becomes uniform. The construction of these curved pieces is simple;
a description of them will be found in the memoir of M. Deparcieux, which43
we have befote spoken of under the article A 7. This contrivance is applied
to the same practical uses as that of the preceding article.
N 7.
The circular motion of the wheel A communicates by the interriiediate
operation of the bar n m, an alternate rectilinear motion to the bar p q, which
is allowed to slide betvveen two clips, one of which is shown in the figure
at t. If the wheel A be used as a fly wheel, the motions will be reciprocal.
The length of the alternate rectilinear stroke made by the rod p q will be
more or less, in proportion as the point of rotation m, is more or less distant
trom the centre of the wheel A.
If the bar p q be taken away, and the bar n m be made to pass through
a circular opening which we will suppose to be made in the clip t, the bar
n m will then have a compound alternate motion, similar to that of the bar
E F G, in our figure L 10. Piate 8. In the first volume of Bailey’s description
of Machines, in folio, we find an account of a silk reel used ih Italy; in
which the guides receive their alternate and horizontal motion by an appli-
cation of this contrivance ; the point marked m in our figure is supported
by a frame which slides in a groove, upon the surface of the wheel A; so
that it may be shifted with facility to any required distance from the centre.
The wheel A is placed in an horizontal position, and receives its rotative
motion by means of an endless band, the constant and equal tension of which
is preserved by providing the wheel A with an horizontal adjustment ; the
wheel is carried by a bar of wood having a sliding motion in a vertical piece
which supports the whole; a suspended weight acts constantly to draw the
wheel A from that which is set on the spindle of the reel.
(07.)
A B in this figure represents a cylinder having a rotatory motion on its
axis; on the surface are cut two spiral channels or grooves similar to 'those
of a screw, their paths round the cylinder are cut in opposite directions, so
that they intersect twice in each revolution, and join or run into each other
at each end of the cylinder ; C is a projecting piece accurately fitted to the
spiral grooves and is attached to the arm C D, which passes through a longitudinal
g 244
groove or passage cut in the fixed cross-frame E P. Under this arrangement
the rotatory motion of the eylinder will produce the alternate motion of the piece
C, by passing alternately from the first or direct spiral groove, to the second or
reversed one. This motion is extremely ingenious, and is capable of extensive
application; it was communicated to us by the inventor M. Zureda, a Spanish
mechanist of great professional merit.
P 7.
A B is a cross frame in which a mortice p q is cut, and in this the spindle of
the pinion n is at liberty to move freely. C D is a bar the periphery of which is
formed into a continued rack and is driven by the pinion, it is attached to the
bar or piece which is to receive the alternate rectilinear motion, and the latter
is made to slide through the clips a and b. When the racked bar C D is carried
by the action of the pinion to the extent of either of its sides, the check-pieces *
and 8 act on the springs rs, ut, which oblige it to retum by its other side.
This movement is difficult of construction: it has been suggested as applicable
to machinery for cutting the tops of piles, but as the teeth of the pinion cannofc
be made of sufficient strength for any engine in which great power is required,
we do not consider it proper for such purposes..
Q 7.. Plan and side Elevation.
ABC, in the plan of this figure, represents a flat circular ring, the inner edge
of which is toothed; D is a toothed wheel which works into the wheel ABC: its
diameter is equal to the radius of that wheel. The bent axle n m pq, revolves
on the centre of A B C; its extremity n supports the wheel D by its centre, while
its other extremity p forms a handle, to which the moving power is applied to
produce the rotation of D; while this wheel revolves on its centre, and traverses
the toothed inner edge of A B C, each point of its periphery will describe a dia-
metepof that wheel. The demonstration of this theorem is given by De la Hire,
in his Traite des Epycicloides, et de leur usages dans la Mecanique. Mein. do
l’Acad. Vol. ix. page 389.45
A model of this moyement was presented at a late exhibition of productions of
tlie National Industry, by M. White. His description of it may be seen in les
Annales des Arts, vol. xix.
R 7.
Two tootbed wheels A and B, arranged as they are shewn in this figure, will
produce an alternate motion, of which the alternations, their extent and velocity,
may be infinitely varied, either by altering the ratio of their diameters, or the
proportions and arrangement of their several parts. These motions may, however,
be accurately produced by the arrangement shewn in the figure A 7.
The combinations shewn in the figures S 7 and T 7 are of the same nature.
An instance of this description of alternate motion may be seen in piate SI, yol. L
of the plates of manufactures of the French Encyclopedie.
U 7. Plan and Elevation.
In the plan of this figure ab c is a flat circular ring, which has a small portion
cut away, and which has a continuous s.eries of teeth formed both on its outer and
inner edges; the portion of the ring which is cut away is of sutficient width to
allow the pinion d to pass freely from the outer edge to the inner, and after
having made the Circuit of the inner edge, to pass at its opposite extremity again
to its outer edge, and the ring is fixed to the circular disk or piate D, which has
a motion on its axis.
The pinion D has a motion on its axis, and this has also a liberty of motion in
the groove n m; two springs p and q act altemately on the projecting stops or
detents r and s, and so determine the quantity of the alternate circular motion of
the disk D ; this is a modification of the arrangement shewn in the figure P 7.
The alternate circular motion of the disk D is used as*an intermediate motion to
produce the alternate rectilinear motion of the point E: this is effected by means
of an endiess rope which passes round the disk, and over the two fixed pullies S
and T. This example in striet propriety belongs to Section IX : we introduco
it Imre as a judicious method of using an intermediate motion; and lo shew the
analogy which exists between this and the subject described in P 7.46
It would be difficult in practice to make the pinion d work with equal facility
on the interior and exterior edges of the ring on account of the difference in tlieir
teeth : this diffieulty inay however be avoided in a great degree, by placing two
pinions d one above the other on the sanie axis, and making a corresponding
separation betvveen the planes of the interior and exterior teeth ; so that they shall
act only on tlieir respective pinions, as is shewn in the elevation of the tigure.
A 7' Piate 4.
We have here coinbined two well-known methods ofconverting direct circular
motion into alternate rectilinear motion, by using a bent axle, or a circular plane
inelined to its axis of rotation. M. Prony gives a theory of bent-axles in the
Journal des Mines.
In the fourth volunie, No. 266 of Memoires approuvees par 1'Acadeinie, we
find an application of this axle to the motion of a piston by M. Laesson. The
author gives a very simple mode of constructing an axle of which the erank may
be lengthened or shortened at pleasure.
In Leupold’s Theatrum Machinarum Hydraulicarum, vol. ii. pl. 36, fig. 1 & 2;
and in Ramelli’s work, entitled—Le diverse et artificiose Machine dei Capitano
Agostino RameUi, &c. a Parigi, 1588, figure 57.—This method of the inelined
circle is applied as a motion for pump pistons. An hydraulic wheel turns a
vertical axle which carries an inelined circular plane; the vertical piston rods
have projecting arms with friction rollers, which are supported by the edge of
the inelined plane: in this way the circular motion of the vertical axle of the
water-wheel produces the required alternate rectilinear movements of the pump
pistons. The vertical position of the piston rods is provided for by grooves with
friction rollers. A second projecting arm from the piston rod, which applies
itself to the under side of the inelined revolving plane, operates to assist the de-
scent of the piston and to equalize the motion.
B7'.
The large wheel R revolves on its axle, and three rollers m n p, are placed on its47
surface; a bent lever P GH, the arms of which are set at right angles with each
other, carries a roller p at the extremity P of the arm PG, the action of a
spring or weight applied to the extremity H of the other arm tends to give the
roller p a constant bearing against the rollers m, n, p, which will therefore, by
the rotation of the wheel R, act in succession on it and cause the alternate circular
motion of H ; this will consequently belong to Section IX.: the alternate circular
motion may be converted into alternate rectilinear by means of a fixed pulley f.
This motion hasbeen applied by M. Genssaneto the construction of a contrivance
which lie used as a substitute for lever handles. See Machines approuvees par
l’Academie des Sciences, Yol. vii. No. 442.
C V.
S is a fly-wheel carrying a pinion p; P and Q are two toothed wheels acting
on each other, and P is also driven by the pinion p; n m, st, are two lever
handles set on the axes of the wheels P and Q; m f, s g, are two rods both the
ends of which have free motion, and they are connected by a cross bar fg with
the vertical and larger rod H R, to which they communicate an alternate recti-
linear motion during the regular action of the fly-wheel S:—the motion is
reciprocal.
The application of this movement may be seen in a memoir on a new steam
engine invented by Cartwright, and inserted in the first number of Les Annales
des Arts et Manufactures. Two pins might be fixed on the peripheries of the
wheels P and Q instead of the lever handles; but they are retained for the greater
facility of construction. In No. 25 of the same Journal the Editor proposes a
new steam engine, in which he adopts Cartwrighfs fly-wheel instead of a
beam.
D 7'. Plan and side Elevat ion.
S is a fly-wheel, on one extremity of the axis of which are fixed two ratchet
wheels R R ; within these, two toothed wheels are fitted on the same axis, but
remain at liberty to turn independently on it. Each of these has a click p,48
which is placed in the same direction on each, and on the outer face, so that
they act upon the ratchets only by turning in opposite directions ; P Q is a large
bar which slides between two clips, and dividing itself into two parallel pieces
forms a frame furnished on the inner edge of each side w ith a rack f g and h i;
these are not situated in the same plane, the rack fg being a little distance behind
the plane of hi, so that hi acts on the wheel M, and fg on N. If we suppose
the bar P Q to move from Q towards P, the rack h i will be brought to act on
the wheel M by the effect of its click p, and will communicate a rotatory motion
to the fiy-wheel in the direction shewn by the dart in the figure; the rack f g
will at the same time act on the wheel N in the opposite direction ; but the
click of the ratchet belonging to N does not hold the ratchet during the upward
motion of the rack fg; the wheel N will pass round on the axle independentlv,
and will not therefore impede the progress of the fly-wlieel in the direction already
given it by the action of the wheel M. When the frame returns from P towards
Q in its descending stroke, the click of the ratchet belonging to the wheel N is
in action, and operates to hold the wheel N, so that the rack f g turns it together
with the fly-wheel, in the direction shewn by the dart as before. If one of these wheels
M or N, together with its rack were omitted, the direct motion of the fly-wheel
would nevertheless continue as in the movement G9; but as the action of the
moving power upon the fly is in that case unequal, the mechanism in the state
here described is preferable. No reciprocal action takes place in this instance.
OBSERVATION.
IF a wheel having a constant motion in one direction by the action of any
mover, receives another wheel on its axis which is held there by its friction only,
being capable of motion on the axis independent of the first, any method which
might be invented for alternately attaching and disengaging the first wheel,
might also be used either to communicate to the latter the action of the mover,
or to withdraw it from such action; in the latter case, it will remain at rest, if
by its inertia, or the resistance it is enabled to offer to the second wheel, it
could overcome its friction; or it will obey the action of any other power tending49
to give it motion. It is thus we are enabled to suspend the opcration of a
machine, without the necessity of interrupting the action of the first mover,
or to withdraw it froin the action of the original mover, in order to connect
it with some other. We find this occur in the action of bells. We shall
give an account of some ingenious methods of releasing the ram of the
pile driving engine, although we consider the arrangement shewn in the
figure I V as the most simple and effective, and one which may be univer-
sally adopted with advantage. We shall however first shew the methods
which may be employed, lst to check the motion of the machine while the
action of the mover is suspended, without subjecting it at the same time to
any effects of resistance ; 2nd, to avoid the accidents which so frequently
occur in ali machines which are required to produce great power, such for
example, as capsterns, presses, the machines used for cleansing harbours, &c. &c.
whenever from violent shocks or other causes the resistance causes a retrograde
motion upon the mover, and communicates it to the machine, or when the
cables, chains, &c. by meafts of which the action of the machine is trans-
mitted to the resistance, liappen to meet with fracture or derangement, and
the machinery thereby acquires a greatly accelerated movement in that di-
rection ; 3rd, to avoid the vexatious consequences which resuit from such
derangement in any part of the machine, whether from natural obstacles or
such as accident or ignorance may occasion, as place the resistance beyond
the powers of the machine to overcome.
In order to check the motion or action of the machine, during the sus-
pension of the action of (the first mover upon it, without subjecting it at the
same time to the effects of the resistance, it is usual to employ a ratchet
wheel with a click which puts it in action, while it operates to check the
action of the mover in a gradual manner, as is effected in the ordinary
methods of working the capstern, &c. &c.*
* In the 14th Report of the Sociefy for the Encouragement of Arts, &c. for 1815, we find the descrip-
tion of a very singular click and ratchet movement, invented by M. Dobo; M. Borgnis, in his work
entitled 1,1 Traite de la composition des Machines,” places it as the 17th variety, 4th species, lst genus,
2nd class, 5th order—Regulators.
II50
When the resistance is thrown on the mover, the retrograde motion of the
machine gerierally produces so considerable a shoek, that the attempt to
counteract it by iulerposing any firm resistance similar to that produced by
the common click and ratchet movement, becomes not merely useless, but
even dangerous; in sucli cases, the most proper course, is to effect a gradual
weakening of the shoek, for which purpose no method can be used which
is in our opinion so likely to be effective as the retarding force of friction,
applied by a check or curb, either to the axis of rotation, or perhaps more
advantageously to the surface of a drum or barrel of considerable size, fixed
on that axis. An arrangement of this method is adopted in England for
lowering heavy weights from considerable heights to which they have been
raised by machinery; this contrivance is curious and judicious ; its description
is as follows.
Let A Figure 1 of Piate 12, represent a toothed wheel, which is driven by
a pinion B immediately connected with the moving power ; the weight to
be operated upon is suspended at the extremity of the rope D, which passes
over the fixed pulley shown in the figure, and returning thence is gathered
up on the axis C of the wheel A ; t represents one of the pivots of that
wheel ; the check is composed of the lever mn, moving on its point of ro-
tation or fulcrum q; to the longer arm m q is fixed the pad or cushion p,
this presents a concave surface to the axis C, on which it may be pressed
by the lever, the counterpoise H serves to raise it from the axis, and the check
pin shown at r, stops it at a convenient elevation.
When it is required to release the weight suspended by the rope D, the
pinion B must be withdrawn from the wheel A, or thrown out of gear, or
it may be detached from the action of the moving power by the method I 7';
the weight will then be rapidly lowered, and when it has arrived within 3 or 4 feet
of the ground, where from its accelerated velocity it would be dashed to pieces,
the operator presses down the lever by its extremity m, with considerable force
and so brings the cushion p to bear on the axis with so much friction as im-
mediately to counteract and check the progress of the falling body.
In a work entitled “ Traite elementaire de Mineralogie,” by M. Brongniart,51
vol ii, page 302, we find the description of a drum-wheel, the motion of which
may be iastantly checked when circumstances require it, whatever may be the
effort of the moving power: by means of a eurb composed of two stays or clips
similar to that already described, and which together form a sort of large
nippers, the spreading of the extremities of the arms of these clips or nippers,
renders it necessary to place a small capstern in the middle point of their separating
distance ; this capstern is worked by the operator when he finds occasion to check
the action of the machine.
The following description will explain the method of tightening the curb.
Let A, Figure 2, Piate 12, represent the drum-wheel set on the shaft or
axis of the machine, this wheel has on one of its ends a ratchet wheel R,
and it revolves on its axis in the direction indicated by the dart shewn in the
figure ; m n is the lever of the curb ; p the cushion; c c a click suspended
by the rope f, to the extremity b of the lever a b, which moves on the
point a, as a fulcrum, and rests by its arm on a small roller which is fixed in
the end m of the lever n m; the timber frame F has a projecting point s,
which prevents the click from rising or leaving its position, while the spring v
acts to press it forward to its operation on the ratchet-wheel, and by its
curvature, keeps it up to its proper bearing while it is in action. lf the
motion of the drum-wheel should be reversed the click will be drawn into
immediate action on the ratchet-wheel, the lever n m will operate to press
the cushion p on the surface of the drum-wheel, and the motion of the
machine will be checked without violent shock, and consequently with the
least possible inconvenience.
Let us now suppose the machine to be rapidly drawn in the direction
of its motion ; and (in order to avoid the unnecessary multiplication of figures)
let the drum-wheel A in the same figure be imagined to tum in a contrary
direction to that indicated by the dart; it will be necessary to suspend the
action of the spring v on the click e c, by means of a pin, so as to allow
it liberty of motion, and so that in case of any sudden and extraordinary
acceleration, the check pin shall cease to act on the spring, and the action
of the machine shall be checked as in the preceding case ; for this purpose
h 252
the regulator N V Piate 5, and the motion G 8, of the same piate may be
used ; the wheel A of this motion represents the drum-wheel A of fi gure 2,
and the spiudle of the regulator may be represented by the axis of the
wheel B, of the figure G 8, Piate 5, and which should be placed in the
upper part of the wheel A, figure 2.
The tension ot the rope Q which communicates the action of the mover
to the resistance, may also be appfied to profitable use, by using it to keep
the click c c in its detached situation with respect to the ratchet-wheel ;
when iu the event of the rope breaking, the click will be instantly released
from its detached position, and will be submitted to the action of the spring r,
which forces the click into action with the ratchet-wheel; the mechanism of this
contrivance will be less complicated than that of the preceding article, and its ac-
tion quicker; it consists simply of a very small cord d d, which is attached by one
end to the lower part of the spring r, and by the other end to a small bar g g,
which slides between the clips g' g', the bar carries a small roller t, which is so
adjusted that the rope Q may press strongly against it, the cord dd is extended
between the bar g and the spring, by small rollers, as shewn in the figure; it will
be evident that if the rope Q should be broken, the roller t will be instantly
released from the pressure which enabled it to hold the click c c from its*
action, the click will therefore as quickly be forced into immediate operatiori
on the ratchet, and the motion of the machine will be checked.
The machine represented in Figure 3, Piate 12, is much used in the
neighbourhood of Paris for the purpose of raising large masses of stone from
the quarries. The celebrated machinist, M. Martin, considered that the
adoption of this machine would prevent the disastrous accidents to which the
workmen in that employment are so much exposed ; its construction is thus.
A lever p q composed of a stout plank, is suspended on the fixed point a,
as a fulcrum ; the shaft of the wheel A passes through the plank at the
point c, and a counterpoise Q capable of raising the wheel A is suspended
at the extremity q ; the machine in this state resembles in its general features
the common steel-yard, on which the wheel A occupies the place of the
mass to be weighed, and in which the usual moveable weight is superseded53
by the counterpoise Q ; in the arrangement of our machine however, no equili-
brium is produced, it being necessary that the counterpoise should exceed the
load. B C is a strong upright pillar, and f e an edge piece of timber which has
a motion on the point f as a centre, and carries the cushion q; e d is a bar either
of wood or mctal, having motion on the axis of rotation e and d; nn is the
rope by which the masses of stone are broughtfrom the quarry P; r is a ratchet
wheel fixed to the axis of the wheel A-, and r its click which is attached to the
upright pillar B C. It will be evident that an upright piece corresponding with
D E must be placed on the opposite side of the wheel A, in order to support
the axis of suspension a of the lever pq; and also, that the latter must be
forked, and its sides at a sufficient distance to allow a space for the free passage
of the wheel A. The mass required to be raised must be attached to one of the
ends of the rope n n, and on the first action of the weight upon the wheel A in
the direction indicated in the figure by the dart, the short arm of the lever p q
will descend, together with the wheel, until the end p of the lever is checked by
some firm resisting obstacle, on which it will rest: the cushion p will be raised,
and the working of the machine will proceed without any interruptiori ; it may
however be suspended at pleasure by means of the ratchet wheel, and whenever
the rope n should happen to break, the wheel will instantly be raised by the
action of the counterpoise Q, the cushion q of the curb will descend and apply
itself upon the drurn wheel, and the shock will be prevented.
In Bailey’s vvork already spoken of under the head E 4, we find in the first
volume page 146, the description of a erane invented by Mr. Pinchbeck. In
this machine a curb is brought into action for the same purpose, but the nre-
chauism is much too complex for general adoption, even if it were fully equal to
the proposed ohject. The rnover which operates to press the curb against t!re
wheel, is the action of large bellows which are worked by machinery.
Whenever the resistance of a machine exceeds a determined lirnit, the action
of the mover may be checked in the followingmianner:—
In the figure 4, piate 12, the lower or shaded figure represents a longitudinal
section of the parts of the arrangement to be described, and the three upper or
outline figures, transverse sections of different portions of the same,54
Let M be the axis or spindle acted on by the moving power, and N that which
is connected with ali the other parts of the machine: now it is required that
whenever the resistance encountered by the machine exceeds the assigned limits,
its safety shall be sccured by the facility of checking it without the necessity of
interrupting either the action of the moving power, or the connection between
the two axes M and N.
A A is a circular piate of iron fixed upon the spindle N: the surface which is
turned towards N is flat, but on the opposite side are formed the two projecting
rings n n and m m.
B B is a second circular piate of iron—on the side nearest to the piate A is
formed a projecting ring p, which fits easily into the cavity formed between the
piate A and the piece b; on the opposite side are two projecting pieces a a,
intended to act against the projections ss of the piece C ; and a strong projecting
stud b, which extends beyond the opposite surface, enters the space formed
by the ring or circular spring D D; performing the office of the curb.
D D, is a ring or circular spring which clips or holds upon the neck formed by
the edge of the piate A and its projecting ring m m; this ring or curb may be
closed or tightened at pleasure by means of the key E, (see the upper or outline
figures) and consequently will encrease or diminish the friction, according to the
required or convenient degree of resistance, in order that the motion of the spindle
N shall be stopped while that of M shall remain at liberty to proceed. When
the communication between M and N is completed, by means of the piece C
which turns with it, and is at liberty to slide in the direction of its axis, (as in
the wheel C of the figure I 7', piate 4.) ; the projecting teeth ss act on the pro-
jections a a, the piece B and the curb are in action, and the whole moves together.
When the piece C is withdrawn from the piece B, the connection of the pro-
jections ss and a a ceases; and whatev er may be the resistance of N, the action
of the moving power on the machine is suspended.
It is evident that if the key E be firmly closed, and the communication between
the two axes be completed by advancing the piece C as directed, the axes M
and N will act conjointly as if composed of one piece; but if by withdrawing the
piece C, we detach them completely, the axis M will in its retiring motion take55
with it the piece B and the curb D D, but the axis N will remain at rest; there-
fore if the key E be just closed so much as that the axis N may be at liberty to
turn, the object of the arrangement will be accomplished with facility.
A very ingenious and important application of this mechanism has been made
by M. Bettancourt in a machine constructed by him for cleansing the harbour
of St. Petersburgh.
In our article L V, will also be found a method of securing a machine from
any hurtful or inconvenient efFect of the action of the moving power within certain
limits.
A machine for driving piles invented by M. Camus.
The ram A is attached to the extremity of a rope which passes over the
pullies B and C, and is afterwards wound on the vertical cylinder D, which with
the lever I, compose the principal part of the machine: its action depends on
the manner in which this cylinder is arranged and acts with the capstem, of
which it forms a part; the capstem and the cylinder are of the same diameter and
are set on the same axis; the cylinder should be encircled orbound with an iron
strap E F, from which should project two or four points or pins also of iron.
The capstem G supports the lever H I, which carries a curved piece or heel
F,	which applies one of its ends against the cylinder, and the other end is attached
to the capstem by a joint or hinge, so that it may be lowered by pressing upon
its extremity I, and raised or kept up to its position by the spring L. The
machine is put in action by applying the power of men to the horizontal levers
G,	M, N, P, who by their means tura the capstem G, and also the cylinder D,
which is attached to the capstem by the lever FI applied to one of its iron
pins; in this manner the rope by which the ram is suspended is wound upon
the cylinder, and the ram is raised the height of the upright frame V y. When
it has arrived at its greatest height, the man situated at the end of the bar N,
presses on the end I of the lever I F and forces it down ; the iron pin of the
cylinder which was held by the heel F of the lever being thus released, the cy-
linder is at liberty, and the ram by its gravity rapidly unwinds the rope fiom it»56
surface and descends; the lever IF is now released from the pressure which
held it ciear of the cylinder, and the action of the spring L raises it to its former
position, the heel F becomes again engaged with one of the pins of the cylinder
which is thus again connected with the capstern, and the operation is repeated.
We may here observe that the ram ofthis engine, and ali those which carry the
suspcnding rope with tliem in their fall, lose a considerable portion of their mo-
mentum by that circumstance.
(F ?.)
The upper figure of the view of this machine represents a side elevation;
and the lower figure an horizontal plan of the central part of it.
An iron spindle p q, turning constantly in the same direction, is shewn in
the side elevation: this is moved eitlier by the power of raen whose action is
applied to the bars of a capstern, or by any other suitable mover: it passes
through two drums or cylinders of wood A and B which are not fixed to the
spindle, but are fitted easily upon it.
The lower drum or cylinder A rests on the bottom board or floor of the
machine: itis formed at its upper part of two rising surfaces abc, a'Ve', one
of tliem on the exterior of the figure, the other on the interior, each making
one tum of its circumference, similar to a hollow screw, or an open and winding
staircase formd of one continuous inclined plane. These surfaces are so arranged
that each has its origin a and a', and also its termination, at the two extremities
of the same diameter. This lower drum A has a ratchet wheel r, and a click s
(shewn in the lower figure) which acts to prevent the ratchet from turning in the
direction of the moving power.
The upper drum B is hollow, and is furnished with twovertical arms orbars
n m, each having a small roller at its lower extremity, the length of the bars is
equal to the lieight of the lower drum ; the upper drum is supported by these
rollers upon the inclined or spiral surfaces formed on the lower drum, and by
which it always preserves an horizontal position. The upper drum also carries a
strong bar of iron terminating at the height of the lower surface, and its outer
surface is grooved to receive the suspending rope of the ram.57
When the rollers of the arrns n m are situated at the commencement of the
inclinet! planes of the lower drum, the upper drum is at its lowest position or
point of d escent, and if it is then turned in the contrary direction to that which
we suppose the moving power to take, that is to say, in the direction cba, the
two rollers will meet the heads of the rising planes and ohlige the drum A to
turn in the same direction. But if B be made to turn in the direction of the
mover, A will remain at rest, and B, turning by means of its rollers upon the
inclined planes will be raised to their height.
The iron spindle p q, has a strong cross-piece i i' also of iron, placed so that
it nearly touches the upper part of the cavity of the drum B when it is situated
in its lowest position.
This description being clearly understood, the mode of producing an alternate
i*ectilinear motion from the direct circular motion produced by the moving power
upon the spindle pq, may he explained in few words. We will suppose lst
the drum B to be placed at its maximum of descent—2nd the cross-bar i i, in
contact and ready to act on the upright bar t—3rd the ram M, resting on
the head of the pile—and 4th the rope d d' in a state of tension; the spindle p q
will in its own rotatory motion carry with it the drum B; this will raise the
ram of the engine to an height equal to the circumference of the drum;
the bar t will then pass the cross-bar i i, and the drum B, thus subjected to the
effect of the ram M, will turn rapidly in the opposite direction and suffer it
to fall. The drum B will consequently have an alternate circular motion while
the ram M will have an alternate rectilinear motion, and it will traverse a space
equal to the circumference of the drum B.
If all the parts of the maehine be supposed in their original positions, and the
lower drum A be turned half a revolution, in the opposite direction to that of
the mover; in this case, when the upper drum B has also made half a revolution,
the ram M will fall; the extent of the circular oscillations of the drum B, and
those of the ram will be thereby reduced one half.
This very ingenious mechanism admits of firmness and simplicity of construc-
tion, and possesses, as we have shewn, the further advantage of allowing the
i58
ramto traverse any required distance from the smallest to a quantity equal to
the circumference of the drum B.
G7'.
This figure includes two views of the machine—one a front, the otlier a side
elevation, the same parts being respectively marked with the same letters of
reference.
A B is a spindle which is turned by the moving power always in the same
direction ; the wheel C, grooved on the edge, fits easily on the spindle A B so
as to be at liberty to revolve with friction, but is not allovved to traverse on the
spindle ; on one of its faces is fixed a check-pin s; n m is an elastic bar or arm
fixed tothe spindle AB; r is an inclined plane placed a small distance beyond the
circle C, and in the same plane ; the rope c t has one end fixed in the grooved
edge of the wheel C, and the other is attached to the flail or beater pq, which
moves easily on the pivot p.
When the spindle A B revolves, the elastic bar n m meets the check-pin s,
and obliges the circle C to revolve, which raises the beater p q: the bar n m
also encounters the inclined plane r, and being thus forced from its contiguity
to the circle C, suffers the check-pin s to pass; the circle C is immediately sub-
jected to the action of gravity of the beater—which falis—and the process is
repeated.
This arrangement, which is in reality but a modification of that shewn in our
figure E 1', has been applied by M. Dubuisson to a machine for beating or
pounding plaster: a description may be seen in the “ Collection des Machines
approuvees par l’Academie des Sciences.” Vol. vi. No. 407.
H V.
The following description of this machine is extracted from the report made
by Messrs. Prony and Molard, upon proposals relative to the re-establishment
of the machine of Marly: printed by order of the National Convention at Paris>
in the third year of the French Republic.59
DESCRIPTION OP WHITE’8 MACHINE.
Page 15—The following is a description of the detent wheels: “ The piece A
is fixed to a spindle whieh revolves constantly in the same direction; and the
wheel B is fitted on the spindle so as to be capable of being turned upon it with
fnction, in the contrary direction. This wheel is furnished with a detent C, to
whieh the piece A catches, and thus elevates the chain D, to whieh one of the
pump pistons is attached: this continues to rise until the detent C arrives at and
presses upon the check-pin E; the piece A is immediately released from the
detent, and the piston whieh is attached to the chain D descends by its gravity,
at the same time causing the wheel B to revolve on the spindle in its reverse
direction.”
17'.
AB is a spindle, whieh we will suppose to revolve constantly in the same di-
rection by the action of any moving power; C is a toothed wheel whieh is fitted
on the spinde A B so as to have the liberty of revolving on it with moderate
friction; and ab are two mortice holes to receivethecheck-pins m and n ; D is
another circle or wheel also fitted easily on the portion p q of the spindle A B,
whieh instead of being circular as in its other parts, is there made quadrangular.
The two check-pins m and n, are fixed on this wheel; and the forked lever f h,
is used on the fulcrum r to force it to or from the wheel C, and consequently to
place the check-pins m and n into their respective mortice holes, or to withdraw
them at pleasure.
Every part of the machine being situated as represented in the figure, it will
appear that the wheel C may either remain in a state of rest, during the action
of the spindle A B, being prevented from accompanying it in its rotation by some
external check: or it may obey the action of another mover whieh shall urge
its rotation in a direction contrary to that of the spindle A B; in short, it may be
considered as really independent of the motion of the spindle, except insomuch
i 260
as it is connected with it by tlie quantity of friction with which it is fitted to it:
but if, by means of the lever fh the wheel D is moved so as to force the cheek-
pins m and n into the mortice holes of C, the latter will necessarily obey the
action of the spindle A B, until D, with its pins m and n, are agam withdrawn
from C, and so on. The action of the spring c is upon the extremity h of the
forked lever, tending to withdraw the wheel D from C; the detent s t, of which
both a plan and profile are shewn in the figure, moves on the axis i, the check e
on one side, and the spring k on the other, determine the direction, and limit
the extent of its movement; if the forked lever be turned so as to perfect the
communication between the wheels C and D, the spring will be checked by the
detent. When it is required to detach the machine from the action of the mover,
a slight pressure must be made on the extremity t of the detent, the spring c
will act on the end h of the lever, the wheel D will be withdrawn, and the re-
quired suspension effected.
This mode of checking the action of a machine may be practically applied to
several useful ptirposes, as for example: to stop a rnechanical operation at a
required time without the necessity of personal attendance, in the working of
mills when the operation of grinding is complete; or in the weaving-loom, when
the flight of the shuttle is accidentally interrupted.
The first-mentioned of these objects presents no difficulty in the application : it
will be merely required to arrange the weight of a repeating watch so as to act
on the extremity t of the detent, which may for this purpose be rendered deli-
cately sensible.
In mill work, the maehinery may be stopped when the required operation is
completed, making use of the last-mentioned contrivance—to call the attention
of the operator to the necessary adjustment of the detent.
In the operations of weaving, accidental interruptions of the shuttle are of fre-
quent recurrence, by the breaking of a thread, or other unforeseen circumstances.
To prevent the disorder which must otherwise be the consequence of such acci-
dents, the following application of this contrivance is made.—The shuttle frame
traverses with an alternate circular movement, (see the Section A, Figure T, in
the compartment K1', pl. 4.) its axis of rotation being in c passing through the
i61
lower framing of the loom, tlie alternate circular motion of the frame should not
be equable, its velocity being’ required to decrease as it approaches tlie extremity
a of the arc a b, described by its motion ; we will suppose this extremity of the
are to be on the side nearest to the large roller, and that the decreased velocity
at that point is required to allovv sufficient time for the shuttle to pass from one
side of the frame to the other, according to the width of the loom, and the velocity
of the frame is required to be more or less accelerated as it approaches the ex-
tremity b of the arc, in order to strike the vroof. Let an iron rod extend the
whole length of the frame, having a free motion on its axis p, and at eacli end
a bent lever n, p, m, r, which by the action of a spring placed near the middle
of the bar, are constantly pressed forward so as to occupy the situations n' p' m7 r7,
while the shuttle, on arriving at the points which it occupies at each alternation
of repose will force them back to their first-deseribed position n, p, m, r, it will
be seen that if the shuttle meets with no interruption in its course, but passes-
freely, the levers n p m r will not meet the obstacles « and £ when the frame by
its alternate circular motion traverses the arc ab to strike the woof; but, if on
the contrary it is interrupted in its passage, the levers which will then assume
their second position n7 p7 m7 r7 w ill first meet the point or object <* which receding
from its action, will descend, and acting on the extremity t of the detent
will effect the separation of the wheels C and D as already described, and they
immediately afterward meet the fixed check B ; the action of the mover will be
detached from the machine, and the frame will consequently not strike the woof,
which was the object required.
This motion I 1' makes an instantaneous communication of the action ofthe
mover to the machine, which is in some cases seriously inconvenient; it may
be avoided in a considerable degree by the use of the mechanism Figure 4.
The extremely simple contrivance of this subjeet (I V) renders it useful in
mill work to suspend the action of one of the stones of a mill where several sets
of them. are worked by one principal wheel, or where direct circular motion
is to be converted into alternate circular, as in large flatting-mills, and irideed
in almost every machine in which it is occasionaily required to check the action
of the works without interrupting the action of the moving power.63
K V.
This is another modification of the preceding arrangement:—A B is a spindle
which turns constantly in the same direction by the action of the moving power;
the wheel C transfers the rotatory motion to the wheel D, which is fitted b7
friction only on the spindle EP; a pin e projects from the face of the wheel D,
and another projecting pin f is fixed in the spindle E F; the wheel D may be
placed within the action of the pin f, or be removed from it by means of the
lever P Q ; it will be evident by simple inspection of the figure that the action of
the spindle E F may be suspended at pleasure by the requisite adjustment of the
wheel D with respect to the pin f.
L V.
This machine is described in Les Memoires de 1’Institut, and in Les Annales
des Arts & Manufactures; vol. xix. page 181. It is the invention of M. Prony.
The organization of his machine consists in factof an extremely ingenious ap-
plication of the contrivance by which we detach, or communicate at pleasure the
action of the moving power, and the axis of a wheel which is fitted on it by its
friction, and reciprocally.
A large horizontal wheel A B is turned by the immediate action of the moving
power, and drives in eontrary directions the two vertical wheels C and D, which
are fitted by their friction only upon the horizontal spindle E F ; the interior face
of each of these wheels has a ratchet wheel n and m : on one of the extremities
of this spindle is fixed the wheel or pulley G, upon which is coiled a rope or
chain, to each end of which is suspended a bueket, as shewn in the figure.
A frame a a composed of two iron bars, carries two ratchet wheels pandq,
one at each of its extremities, and it is at liberty to slide back and forward on the
square spindle E F by means of square boxes, wdiich are fitted to, and slide
upon it.
It is evident that if the frame a a is pushed towards the end E of the horizontal
spindle E F, the ratchet wheels q and n at that end of it, will be placed In63
action, and the axis E F will then revolve in the same direetion as the wheel D,
but if the frame a a is pushed towards the end F of the horizontal spindle, the
ratchet wheels pandm will be in action, and the axis EF will revolve in the
direetion of the wheel C, and one of the buckets which are attached to the chain
will ascend, while the other will descend. Ali that now remains is to communi-
cate this alternate movement to the frame a a, so that it shall take place imme-
diately afiter the rising bucket has emptied itself into the trough; and so that
the chain of the rising vessel shall itself regulate the movement.
The inventor effects this by placing an horizontal spindle S S below E F,
and in a direetion at right angles to it. This second spindle is of iron, and has
an ann x which projects upwards, and into the sliding boxes ofthe frame a a ;
it has also a long upright arm h, which is surmounted by a weight of lead of
lenticular fbrm, and below are two flat pieces or feet s and t; two forked pieces
are placed near the extremity of the chain, just abovethe buckets, so as to act in
succession on the two levers M and N. Those levers act upon the feet s and t,
elevating them so that the upright bar h declines from a vertical position at the
moment when the rising bucket is completely emptied; the weight P then
produces a quick oscillatory movement of the spindle S S, and its arm x drives
the frame a a towards the end of the machine over which the weight P inclines,
and retains its position long enough to produce the operation of the ratchet
wheels of that end of the spindle as already described. The spindle E F revolves
in the contrary direetion, and so on *.
M. Prony has also contrived a very ingenious method of releasing the animal
used as the first mover, whenever the resistance is accidentally encreased. The
following description of it is inserted in Les Annales des Arts, vol. xix. p. 190.
The traces 1,1, 1, figure f pass through the apertures 2, 2, in the yokes 4, 4,
which are attached to the levers 3, 3, this lever is set in the vertical spindle
which gives motion to the machine; the apertures 2,2, have friction rollers. The
* We find an application of this morement in a machine for rifling gun.barrels, invented by M. Jac-
%uet; a description of which is giyen in Le Bulletin de la Societe d’Encouragement, Scpt. 1817.
«64
extremity of eacli trace terminates in a loop which hangs on a stud or pin, fixed
in the roller 5, which is moveable on pivots. A rope is coiled upon this roller
which afterwards runs over the pullies 6, 6, 6, and is finally attached to the
weight 7.
This weight, which may be varied at pleasure, will therefore regulate the re-
sistance required to be opposed to the effort of the mover: thus—suppose this
weight to have been fixed at 20 lbs. and that any obstruction took place in the
working-part or wheel-work of the machine, it will follow that, without the
assistance of this mechanism, the effort of the animal or mover vvould cause the
derangement or destruction of the machine ; but as the effort of the mover ne-
cessarily exceeds the regulating weight, the roller 5 will be forced to describe
one-fourth of an cntire rotation on its axis; the studs or pins of this roller having
thus left their former vertieal position, the traces which were attached to the roller
by them, will be allowed to slip off, the animal or mover will be liberated, and
the tnachinery will suffer no derangement. This method will also be found appli-
eable to the purpose of preventing animals employed as first movers from exerting
more than a given quantity of power, which can be determined at pleasure by
the previous adjustment of the counterpoising weight 7.
M 7'. Piate 5.
In this figure which is a side elevation of the subject, a b represents a vertieal
spindle which has a rotation on its axis, by the action of any mover applied at a;
its lower pivot rests on a block of wood e, this has two rollers which work in a
groove or channel cut in the cross-piece n' m'; by this means the spindle ab is
brought into contact with the two vertieal wheels F and G altemately, and act
upon them by an endless screvv h. C and L are two cross pieces which support
the spindle ab, at the same time allowing it sufficient space for the vibratory motion
given it by the piece e. On this piece may be observed two click pieces a' b7, c d
turning on the points a' and e, which as well as the two pins or ends b and d
which proceed from their extremities, are of sufficient extent to reach the surface
of the metal piece u m n. (For a more minute and distinet view of these parta65
see the separate and enlarged figure m in tlie margin of the principal figure).
This piece has an jixis g f, from which at about the middle of its length, pro-
ceed at right angles to its direction, the two forked branches i 1, which are in-
tended to conduct the ropes which support the buckets; and near the extremity
g of the arm fg is fixed an upright arm carrying theweight P ; in the cross-piece
will be observed two projecting pins x and y, having the quantity of their pro-
jection equal to the thickness of the two click-pieces a' b', c d; two buckets are
attached to the ends of a rope which passes over the cylindrical backs of the
toothed wheels F, G, taking one revolution on each. The action of the machine
is as foilows:—
Ali the several parts of the machine being in the positions represented in the
drawing, the upright arm u, after having pushed the pin a' towards the left,
throws the endless screw h within the action of the toothed-w’heel F, and the
click piece a' b' falling by its own weight, comes in contact with the pin x, and
throws the spindle and its endless screw into action with the wheel. When the
projecting button s, which is placed a little above the bucket s, enters the forked
piece 1, the piece u n m is obliged to revolve on its axis; and the arm n, Corn-
ing into contact with the pin b, disengages the click-piece before it reaches its
liorizontal position: but on the instant of its passing that position, the counterpois-
ing weight P falling on the other side, the arm u presses on the pin c, and drives
the vertical spindle within the action of the toothed wheel G, while the click-
piece cd descends by its weight into contact with the pin y. The two cylinders
on which are placed the wheels F and G, will therefore move in different direc-
tions, and the bucket S will descend while the opposite bucket rises, and so on
in succession. On the edge of each bucket is a piece of iron which, when the
vessel arrives at the proper height, receives a hook which operates to overturn
and empty it. This machine is invented by M. Bettancourt.
In a work entitled—Branca (Giovanni) le Machine, volume nuovo e di molto
artificio dei Signor G. Branca, ingigniero et architeta della santa casa di Lo-
reto. Rome 1629, 4to. (Italian and Latin.) Figure 21. The author shews
the application of two vertical face wheels fixed on the same axis, and placed
opposite to each other; a horizontal wheel turning constantly in the same di-
x.66
rection, is forced into action with the two wheels alternately, by an assistant.
Thus communicating an alternate circular motion to the common axis of the
two vertical wheels; this method of converting the movement is applied in many
different machines.
N7/.
In this arrangement it will be observed that, in proportion as the rotatory
motion of the spindle ab encreases or diminishes, the weights p and q aredriven
from, or suffered to approach the axis of the spindle by their centrifugal motion,
and the cap r, which fits easily on the spindle, rises or falis upon it; the action
of a steam valve m, is made to depend on this vertical movement of the cap, and
the machine by this means preserves nearly an uniform velocity although the re-
sistance be variable. We have seen this contrivance used with great effect in
England in a wind-mill for the purpose of raising the upper rnill-stone, when
its velocity becomes too great, and to prevent the meal from being improperly
heated. The singular ingenuity of this application will render an account of
it interesting.
The upper mill-stone A, (figure n 71.) receives its movement from the upper
side, as in the usual construction of wind-mills. The stone is supported by the
axis ab which rests on the block C, fixed to the beam D E. Upon the spindle
is fixed the cap fg, which carriesfour arms for the purpose of receiving the stems
of four iron balls h, i, k, 1, each from four to five pounds weight; from the upper
part of the stems four arms descend and support the piece F, which is at liberty
to slide easily the entire length of the spindle; a groove is cut on the edge of
the piece F, to receive the forked end of the lever d, e, to the other end m of
which is suspended one extremity of the beam D E, its other end being sup-
ported by the jointed bolt n.
It will be evident that the arrangement of balls, here described, will revolve
about the axis, with the motion of the upper mill-stone, and that in proportion
as the force of the wind encreases the velocity of the mill, the balls will encrease
their divergency from the axis; the piece F will descend, will consequently
lower the extremity d ofthe lever d, e, m, which having the point e for a fui-67
erum will operate to raise the end E of the beam DE, and consequently the
upper mill-stone A.
This mechanism has been applied by INI. 0’Reilly, in his blowing engine.—
Annales des Arts, vol. x. page 26.
InBockler’s work, already mentioned, under the article E 3, figure 19, wefindthe
description of a mill which is putin motion by theaction of a horse : in this mill we
may observe a piece of mechanism which is used for raising or lowering the upper
mill-stone. This mechanism differs from that before described in that the lever
d e m, instead of being parallel to the beam D E, is placed perpendicular to it;
and that its motion does not depend on the velocity of that of the mill. The
author simplv suspends a weight to the extremity d of the lever dm, and which
he adjusts at pleasure as to its distance from the point of rotation or fulcrum e,
(as in the case of the common steelyard) for the purpose of regulating the distance
of the mill-stones; but the interval remains uniformly the same so long as the
position of the weight remains unaltered. In figure 47 of Bockler’s work, he
shews an application of the same mechanism to a water-mill.
R amelli, in his work already mentioned in our Article A 7', figure 120, had
before this made a similar application of this mechanism.
O 7'. Plan and Elevation.
The description of a mill which is worked by the operation of the flux and
reflux of the tide, invented by Leslie of London, is given in Les Annales
des Arts et Manufactures, vol. xxii, page 302. The operation of this mill
being simply to convert an alternate reetilinear motion, into a direct circular
motion, we shall merely insert its description as it is given in the work
mentioned.
Figure 1—Is a horizontal plan or section of the wheel, with its outer cover or
case.
Figure 2—Is a vertical section.
a, represents the spindle or shaft of the wheel revolving on a pivot of metal
which works in a bed of steel.
k 268
b b, are wings of the wheel, a little inclined so as to admit the influx of the
water in a spiral direction.
c c, A drum or cylindrical case, within which the wheel revolves, leaving the
smallest space possible betvveen the partitions and the wings.
dd dd—A second drum or case of larger diameter, placed above the wheel,
and forming an upper structure to the drum cc, with which it is also connected.
e e—moveable shutters, opening on opposite sides : the first, which is on the
side in the direction of the current, opens by the pressure of the current, and
is stopped at its proper position for that purpose by an upright timber f; the
shutter of the opposite side will of course be pressed by the action of the current
in the opposite direction, and will therefore be closed by the same action which
opened the first. The inverse of this operation will take place, when the water
which has risen during the tide of flood or increase, seeks egress at the tide of
ebb : the dotted lines of the figure will sufficiently indicate this reverse movement.
Now, let us suppose hh in figure 2, to represent the surface of a river or
current which is at the level of the cover of the upper drum or compartment at
the ebb-tide, so that there shall be the same quantity of water always acting on
the wheel if the surface of the current should happen to be above the upper edge
of that compartment, the w ater which runs above, even if elevated several feet,
will not produce any greater effect than when it reaches but to the level of the
cover.
Let i i represent the bed of the river, and if it has not sufficient depth, it may
be encreased by digging *. The current penetrates the drum by the opening e,
causing the latter to rest itself against the cheek f, by this admission it passes to
tlie lower side of the machine by traversing the spiral wings of the mill, which
are thus put in action by the impulsion of the current, and produce a rotatory
motion of the vertical spindle; the current having passed through the machine
* We consider this practice as entirely inadmissible—for the resistance wliich the running water will
meet with froia that portion of the column which is at rest, will diminisb its velocity, or eren reduce It
altogether.69
and reached the bottom, escapes by the opening or shutter k; this is the process
during the tide of ebb: on the contrary during the tide of flood, the shutters or
openings mentioned, (k and e) will close, and the opposite ones w ili be opened,
by which the water or current will descend as before, and the wheel will continue
to turn in the same direction whether the current be that of the ebb or flood
tide.
The peculiar advantages of this wheel over those of other contrivances for tide
mills are these:—
lst—It is to be preferred for a corn-mill on account of its velocity being more
uniform, from the circumstance of its motion being produced by the constant
action of the same quantity of water.
2ndly—It has the peculiarity of its motion being produced constantly in the
same direction, whether by the flux or reflux, and in. a much more simple manner
than Ln other tide-mills.
3rdly—The wheel being liorizontal, it is very easy to adapt and fix any required
wheel-work upon the spindle, the spiudle being easily raised above the surface
of the water.
4thly—This wheel has a greater velocity with respect to the velocity of the
acting current, than other wheels of the same description ; and this circumstance
enables us to dismiss all the contrivances practised in the old wheels to couiiteract
or diminish friction.
With respect to the construction, the inventor States that its simplicity ishighly
favourable to economy in the first cost.
We find descriptions of many different mills which act by the same moving
power, in 1’Architecture Hydrauli que de Belidor,
P 7*. Plan and Elevatione
In the upper figure or elevation, A' B represents a fixed vertical axis or pillar
of very solid construction : it is surmounted by a toothed wheel C. A hollow
cylinder D is placed upon the axis, and rests upon a projecting ledge at its
lower part. Four cross pieces ab, c d, e f, gh, project horizontally from the70
cylinder D, and are placed at riglit angi es with each othcr; at tlie extremity of
each of these cross pieces or arms is suspended a commodious seat or chair,
and upon the face of one of the arms (ab) is set a small toothed wheel D' re-
volving on its axis, and working with the wheel C. The wheel D has a small
lever handle E from the upper extremity of which proceed four ropes, each of
thern passes over a small fixed pulley, and they are fastened at the extremities of
their respective arms.
A person seated in one of these four chairs ean easily communicate a direct
circular motion to the small wheel D(, by means of the rope, w hich passing over
the pulley is situated directly in front of the seat, and by applying an alternate
rectilinear action to that portion of the rope * he willbe himself carried round with
a circular movement which will include the entire moveable part of the arrange-
ment of which he forms a part, and which will thus composea sort of fly-wheel.
It w ill always be in his powerto vary or modify at pleasure the velocity of tliis
direct circular movement of the machine.
If instead of one person, we suppose two, three, or four persons to be seated
in the chairs, it will be necessary for them to apply the action in concert, so that
they do not counteract each other.
This ingenious machine was invented by M. Marcel Cardinet, and was se-
cured to him by brevet of invention or patent; his object in the invention w as
the material improvement of a popular amusement, by dispensing with the
manual labour by which the machine was then impelled, and affording the
parties themselves the important advantage of regulating their velocity, and
of stopping the motion of the machine at their pleasure.
Before this application by M. Cardinet, the same mechanismhad been applied
to the construction of a watch by M. Breguet, in which the regulating parts re-
volved about an axis, under such an arrangement, that the relative positions of
all its parts were continually changed; and this, as the inventor conceived, af~
forded an effectual remedy for many serious inconveniencies and imperfections
^ Similar to the action used in rowing.71
of watclies of the usual construction. The application of the idea to this practical
purpose was worthy the reputation of an artist of his distinguished inerit: bnt
certainly the coineidence of invention does not lessen the inerit or impeach the
ingenuity of M. Cardinet, wrho, as wefully believe3was unacquainted with M. Bre-
guet’s invention; it affords a very remarkable instance of the relation which
Science establishes among branches of knowledge, where to snperficial observers
tliere seems no analogy.
Q V. Piate 11.
Let A represent the plan or upper side of a wheel having a ratchet wheel
abc d on its face of tlie same diameter ; e f and d g are two arms, which areeach
at liberty to turn freely, by one of their ends on the axis of the wheel A ; f g and
h g are two other arms forming with e f and d g an irregular quadrilateral
figure, of which the angles at f and g are nearly right angles; the several ex-
tremities of these anns are United by centre pins upon which they are at liberty
to turn freely; h i is an arm connected with the quadrilateral arrangement
of bars already described, by its extremity h; the three arms h i, hf, and h g,
are also held by a centre pin upon which they have free motion ; the arm h i
passes through the clips k and 1, and is therefore confined in its movements to
the direction in which they are placed; the tw o arms e f and eg carry two click
pieces m and n, one of them placed to the right, the other to the left of the
figure; these two click pieces are connected with the arms by hinges, and they
enter, and are kept to their action in the notches of the ratchet wheel, either by
their own weight or by the operation of a spring. If now the arm h i be
moved in the direction h i, the click piece m will act upon the ratchet wheel,
and cause the wheel A to revolve in the direction indicated by the dart in the
figure, while the click-piece n will slide over the teeth of the ratchet wheel ;
but if the arm hr return from i towards h, the click-piece n will then act,
while the other piece m will slide over the ratchet; in each of these cases, the
wheel A will revolve in the same direction. The alternate rectilinear motion of
the arm h i will thus be converted into the direct circular motion of the wheel A,72
R7'. Piate 11.
Let A represent a wheel from which there projects the six pins 1,2,3,4,5,6;
and hp a horizontal bar supported by the rollers B and C; the bar hp has a
projecting piece DE, the length of which is equal to the distance d e, between
the bar hp and half the arc 1, 2, which separates the pins 1 and 2; PGH is a
bent lever composed of the two arrns F G and G H placed at right angi es to
each other, this bent lever is at liberty to tum freely on the joint G, the length
of the arm G H is equal to the radius of the circle A, the centre point G is
situated in a line G K, drawn through the centre K and parallel to the bar h p,
and the arm HG tends constantly to descend by its weight; f is a pin or check
which is attached to the bar h p, the horizontal distance of this pin upon the bar,
from a vertical line drawn through the joint G, is equal to the distance Dd.
Now, if under these circumstances, the wheel A be made to tum in the direction
indicated by the dart in the figure, the pin 1 acting against the projecting piece
D E will draw the bar h p from h towards p, while the pin 5 will raise the bent
lever F G H; when the pin 1 arrives at the point e, its action on D E will cease:
the arm G F of the bent lever FGH is then in a vertical position, and will begin
to act on the pin f of the bar h p, which will therefore make a retrogade hori-
zontal motion in the direction p h; when the pin 5 of the wheel A arrives at ‘
the position 6, it quits the arm GH of the bent lever, which falling by its
weight rests on the pin 4 which is then in the position 5, the pin 6 at this time
occupies the position 1, and the same alternated motion is repeated, so that at
each entire revolution of the wheel A, the bar h p makes six movements to the
right, and six to the left. We find this contrivance adopted in a machine for
polishing clock springs, described by M. Thiout, in his Treatise de 1’HorIogerie
Mecanique et Pratique; printed at Paris 1741. Vol. i. page 85; the same work
.also contains descriptions of several clock and watch scapements.
S 7' and T 7'. Piate 11.
These two contrivances for converting direct circular motion into alternate73
rectilinear, afford an approximating solution of the problem. They are some-
times adopted in the construction of steam engines.
In the figure S 7', nm is the crank of an axle n, which receives its circular
motion from the first mover, D is a bar attached to the extremity p of the piston
rod of a pump, and which will then traverse on the line b b a distance which
approximates to twice that of the crank arm n m. The lengths of the arms
B and C, and the position of the centre of rotation F, is arbitrary. The bar C
is placed in the three positions Ft, F q, and Fr, which it will oocupy at the
middle and the extremities of the course described by the point d of the arm D;
this will determine q, r, and s for the points of oppositiori which the other end
of the bar B will have at the same time ; if a circle be described through these
points, its radius will be the length of the arm A, and its centre, the point of
rotation. A few repeated trials will be found to afford results sufficiently accurate
for practice.
In the figure T 7' are also given the lengths of the arms EIH, and the point
of rotation F ; the points n, m, and r are determined as in the lastexample; and
the radius and centre of the circle which passes through them, respectively give
the length of the arm L, and the situation of K its centre of rotation.
SECTION. VIII.
To convert a given direct and equable circular motion, or the velocify of which
varies by a given law, into direct circular motion, of velocity similar to that
of the moving power, either equable, or variable by a given law, and in the
same, or in different planes.
A 8.
THE two toothed wheels A and B act on each other in the usual manner;
the direct circular motion of the one, is communicated to the other, which is
situated in the same plane, but the direction of the communicated motion is of
course in this instance, contrary to that of the mover; if a motion be required
in the same direction, a third wheel C must be added to the arrangement: the
L74
ratio of the velocities will be detcrmined by tliat of the diameters. If n be sup-
posed to represent the radius of the wheel A, and n' that of the wheel B, and
if n and n' are whole and prime munbers, the two wheels A and B will after
certain revolutions, resume the same relative positions, if the number of revo-
lutions of the wheel A be equal to n', and those of the wheel B be equal to n.
A very ingenious and practical application of this property of circles of un-
equal radii has been made by M. Breguet, the younger, in the construetion of
watches, in the following manner: — the fusee is laid aside in this descrip-
tion of watches, and the barrel or cylinder A, (see figure 5, piate 12.) which
encloses the spring, has a toothed wheel «e, by which the action of the
spring is transmitted to the pinion of the first wheel in the train ; the spring
is attached by one of its extrernities to the axis r d, and by the other to the
interior concave surface of the barrel; the length of the spring is such that
supposing it entirely released, the axis rd may make twelve revolutions to bring
it up to its maximum of tension; in general, the mean tension of the spring
is that which is employed, that is to say, the tension produced by four mean re-
volutions of the axis; the ratchet wheel x is applied to prevent the arbor
from turning in the contrary direction to that in which the barrel is impelled
by the spring; and finally, the advantage of suppressing the fusee results
from the prineiple of the escapement itself: the inequality of the action of the
spring being compensated by the unequal action exerted on the escapement
during its repose. This being understood, the inventor has set a toothed wheel
B upon the axis rd,, acting on a second wheel C, which is fitted easily upon a
cylindrical stud or pin which stands upon the upper face of the barrel, a broad
and flat-headed screw is tapped into the upper end of the cylindrical pin, and
thus secures the wheel C ; the diameters of the wheels B and C, are respectively
as five and four, the wheel B must therefore make four revolutions, and the
wheel C five revolutions, in order that the same teeth of those wheels shall be
in contact and their positions be relatively the same as at the commencernent of
the movement; if the wheel B does not move, which is the case when the barrel
is in action, the wheel C will make four revolutions about the wheel B, in
order to arrive at its point of commencement: it will in that course have75
made five revolutions about its own axis, and tlie same teeth will again be
brought into contact with each other. Now if the spring contained in the barrel
is compleatly relaxed, and that we cause the axis d r, and conseqnently the
wheel B to make eight revolutions in the direction indicated by the dart in the
figure, we shall then obtain the maximum action of the spring; it will aet to
impede any farther revolution of the axis rd ; we will suppose the lower figure
represented in the piate to exhibit in plano, the relative position of the wheels
B and C at that moment; if the distance d e be divided into two equal parts in
i, and the semicircle d fe be described on that point, itis evident that in order
to produce the intended effect to the greatest possible advantage, thestops should
fall into contact in some part of the semicircle d f e ; but when the motion of the
wheel B ceases, the wheel C is made to commence its motion by the action of
the barrel, and imagining the diameters of C and B to be respectively repre-
sented by n' and n, C cannot return to its first position after n' revolutions about
B, because it will previously fall in contact with the stops, in whatever part of
the semicireular arc the point of contact may be determined; but it will meet
them under different angles ; this therefore does not produce the end required.
It is a necessary condition that the stops shall fall in contact at right angles before
the wheel C shall have compleated the number of revolutions represented by n',
about the wheel B. Let f be the required position—it is necessary that the arc
a b should be equal to the arc a c, for if the barrel be turned in the contrary
direction to that indicated by the dart, the point b will fall in contact with the
point C, and when the centre e of the wheel C arrives at g, the angle de f
will equal the angle dgf; and consequently the eonditions will beanswered:
al is the fourth part of the periphery of B, and ak is the fourth part of the
periphery of C; we have therefore
a A=:« k~a 1^‘j
and if we make ali=al and draw through the point h the line d g equal to
d e, and from the point d draw the line d f perpendicular to g e, the inter-
section of that perpendicular gives the position of the point f, in which the stops
p and q must be in contact whatever be the ratio of the diameters of the wheels
B and C ; in this insiance we shall have ah=al£, or the angle gd e=»72 de-
l %76
grees. The position of the point f being thus determined the two stops p and q
will be placed as in the figure. The centre of the wheel C will arrive at
the point g before it will have completed the number of revolutions represented
by n', and the action of the watc-h will be stopped : in order to wind it up, the
wheel B must be turned in the direction indicated by the dart; the wheel C will
revolve on its axis in the contrary direction, and the stop p will be checked
by q, as at the commeneement of the action.
In watches of this description there is no exterior indication by which the state
of the spring may be known, and they are consequently much exposed to the
inconvenience of being unexpectedly stopped, as well as improperly wound up.
M. Breguet, the elder, has contrived the following method of exhibiting the
required indication :—A screw m n is cut upon the axis r d, and the broad nut
s t with bevelled edges, is fitted upon it, one or more arms u project from the
upper surface of the barrel, passing through the nut st and allowing it a free
vertical motion. Now when the watch is wound up, the screw is turned, but is
not at liberty to alter its vertical position, and since the nut s t cannot revolve
horizontally on account of the arms u, which pass through and hold it, it will be
compellcd to rise vertically, that is to say, on the axis rd, as we have already
shewn in our explanation of the action of the nut and screw in the article C 3 ;
but while the watch is in action it is the nut which turns, and it then traverses
the same space in an opposite direction; from this there results an alternate ree-
tilinear motion, which is then converted into alternate circular motion by the ap-
plication of a bent lever a', b', c;, d', whose arms are placed at right angles to each
other; the smaller arm c' d' of this lever rests upon the bevelled edge of the nut
s t; and the longer arm a' b' carries to the exterior of the watch an accurate
indication of the state of tension of the spring; and this is exhibited on the dial
piate by an arc of suitable dimensions.
If the three wheels A, B, and C are of the same diameter, during the time in
which A makes one revolution in the direction pointed out by the dart, the
second wheel B will make one revolution in the opposite direction, and the
third wheel C will also make one revolution, but in the same direction.
We will now suppose the wheel A to be fixed, and the w heels B and C to be77
attached to thc wheel A by a bar or arm—it is evident that if the arm be made to
tum about the centre of the wheel A, when it has completed one revolution, thetwo
w heels B and C, will also have made one revolution, as in the preceding case witli
respect to the wheel A; for the relative eftect will be the same, whether the first wheel
A makes one revolution on its axis, or the second and third wheels makea revolu-
tion on that point; but in the second case the wheels B and C will participate in
the rotatory motion of the arm, an effect which does not take place in the first case.
It follows that the wheel B, whose rotation on its axis takes place in the same di-
rection as that of the arm, will have made two turns or revolutions with respect to the
distance, but the rotatory movement of the wheel C about, its axis is made in an
opposite direction; and consequently by the operation of the moveable arm, it
will have traversed the circle which the arm describes in its motion about the axis
of the Avheel A ; but it has no movement of rotation on its own axis, and conse-
quently any lines which may be described on its surface in whatever position
or direction, will preserve a constant parallelism among themselves.
This arrangement is often applied to the mechanism by which we illustrate the
constant parallelism of the earth’s axis in its motion through the annual orbit.
The machinery generally used in the manufactories of porcelain, for the pur-
poses of pounding the materials, and reducing them to the iinpalpable state in
which they are required for the subsequent processes, consists, as is familiarly
known, of a large horizontal wheel, w hich is turned either by the application of
animal labour, or the action of water; this wheel drives four or six pinions, the
axes of w hich descend vertically, and each is immersed in a circular trough or
vessel AAAA, (see the plan of fig. 6, piate 12, and the elevation No. 1.); at
the bottom of each vessel is fitted a slab of stone which exactly filis the space.
A second stone D, is placed upon the first—this is also circular, and its diameter
is somewhat more than the radius of the lower stone C ; the upper stone D per-
forms the action of a mulier: it is fixed on or held to the lower end of the pinion
by a cramp-iron e d, b c ; plates or slabs of porcelain are sometimes substituted
for these stones, in which case the upper piate D is surcharged or loaded with
some heavier body. The earths and materials which are to be subjected to
ihe operation of the machine are placed in the troughs, which are then filled up78
with water, and tlie process commences: wlien this arrangement has been some
time in use it is found that the stones C and D do not wear uniformly—(ho^e
parts of each of them which are the most remote from the centre of rotation C
are considerably worn down; the acting surfaces therefore nili be no longer
parallel with each other—the parts fngmh will leave a cavity : in order to
remedy this derangement, in some degree, it is usual to fit the cramp-iron
edbc loosely into the upper stone so asto allow it a little shake or motion,
that it may fall to fili up the space occasioned by the wear. This is how ever
but a partial remedy—its operation is to prevent the frequent changing of
the stones. The mulier or upper stone D can never become equally wrorn,
unless every part of its surface traverses equal spaces in equal times ; and this
can be accomplished only by such an arrangement for its motion as w ill cause
any lines drawm on ifs surface to preserve a constant parallelism. The mechanism
which is the subject of the present article is strictly applicable to this case: the
proper arrangement is shewn in the plan, and the elevation, No. 2, of figure 6,
piate 12; the vertical axis passes through the cross piece B B, it is supported by
the flanch nn, and terminates in the arm cb, placed at right angles to the
upper part. From the centre d of the upper stone., a vertical arm d c projects,
and passing through a circular aperture in the arm c b, carries at its upper ex~
tremity the toothed wheel e ; a short pin fh, projects from the middle of the
arm cb, and carries at its upper extremity the toothed wheel h, which is at
liberty to turn freely on it; a toothed wheel g is fixed on the under side of the
cross piece B B, and the axis a b passes and works freely through its centre.
The diameter of the three wheels e, h, and g, are equal.
Another extremely simple and practical method for obtaining the required
parallelism is this. (See the plan, and the elevation, No. 3, of pl. 6.) A cylindrical
arm d e, projects from the centre of the upper stone D, and passes freely through
a circular aperture made in the horizontal arm rb of the vertical axis ab.
Another point f, is taken on the face of the upper stone D, in the same direction
but of somevvhat greater length than cd ; from the point f, an arm f g projects
and passes freely through a circular aperture in the horizontal arm k i of the
axis hi, which is supported by the cross piece B B, it is necossary that the two79
horizontal arms ki and rb should be of equal length. When the axis ab is
turned, the point d of the upper stone describes a circular patii on the centre c,
the radius of vvhich isequal to the distance d c ; the second point f, on the upper
stone, \vili also describe a circle the radius of which f h is equal to d c; these
radii will be constantly parailel, and every part of the surface of the upper stone
will have the rcquired parailel motion.
Eithej* of these methods would produce the equal wear of every part of the stone
D, supposing it tobe homogenous and that the lower stone was similarly circum-
stanced, but unfortunately this is not the case : the eftects of the trituration upon
the surface of C diminish from the centre towards the periphery, its surface will
therefore become concave, but the surface of the upper stone will also alter its
figure, and will become convex ; we are well persuaded that a considerable ad-
vantage would be obtained in the wear of the stones by the adoption of these
arrangements.
Subsequent to our organization of this improvement in the machinery used
in the operation, of pounding or trituration, M. Joseph Zureda has commu-
nicated to us an account of his maehine for polishing glass plates, established
in the imperial manufactory of St. Petersburgh. In this maehine the polishers
are guided in their motion by a contrivance precisely similar to that we have
just described : the arrangement is shewn in figure 7, piate 12, in which abed
is a bar of iron, supported by five cranks e, e, e, e, e, of equal lengths, aud are
so arranged as to preserve parallelism among themselves, while the centre crank
moves about its own axis by communication with the first mover, which in this
maehine is an hydraulic wheel. It will be easily conceived that by the action
of this movement every part of the bar a, b, c, d, will describe a circle whose
radius will be equal to the length of the crank arm. This action allows the
weight to be lightened by suspending it by the ropes ss.
The polishing tools f f f operate on the surface of the plates, and their position,
or that of the plates are altered at pleasure as the state of the process may
require.
B S. Piate 5.
The same problem is resolved by this arrangement, by means of an endless80
rope or chain: the movement takes place in the same, or in a different direction,
according to the arrangement of the rope on the wheels, whether passing over
them without Crossing, or being crossed between them.
The length of chains or cords is subject to continual variation from natural
causes: the preservation of their uniform tension therefore requires tlie appli-
cation of counter-acting weights or springs; but in applying such remedial
contrivances, care must be taken that the power shall act in the same direction
as the first mover, that is to say, that the tension produced, shall act on the wheel
which receives the action of the mover in the same direction as the mover itself;
a counterpoising weight may be employed with good effect under such regulation,
and may be applied with success to any machine; but if the tension produced by
its operation acted in a contrary direction to the motion communicated by the
moving power, the effect would be destroyed.
The forms of chains vary according to the purposes to which they are applied;
a detached account of several may be seen in the French “ Encyclopedie,”
under the hcad—Chain-making ; and in Les Annales des Arts et Manufactures:
No. 41, page 213, we find a description of a chain invented by M. Hancock.
C 8.
In this figure are combined different methods of communicating the motion of
wheels in the processes of the arts.
D 8.
This figure shews an endless screw, which transmits its direct circular motion
to a wheel. The action of the mover is perpendicular to that of the wheel; the
practical applications of this movement are extremely numerous and familiarly
known.
E 8.
The silk-mill of Piedmont, presents a remarkable specimen of the application
of the endless screw—the screw is in that machine of unusually large diameter.
In the figure, A B represents the diameter, and the single thread of which it is
composed is divided into six equal parts, which are arranged between the two
parallel planes of the figure; these separated portions of the spiral arranged in81
echelon upon the periphery of tlie wheel, are represented in the figure by the
double curved lines ab, ab, ab, the rotation of tlie wheel causes them to
act in succession on the cylinders H of the machine, by means of the six
rollers or teeth de, de, &c. fixed on their peripheries.
A detailed description of this machine may be found in La description des arts
et Metiers, published by the academy of Sciences.
P 8.
The sarae problem may also be resolved by the means of bevel wheels,
represented in the figure by the truncated cones A and B. Tbis mechanism
is of frequent application in the arts, the figure shews a familiar instance,
in the common carpenter’s wimble. The theoretical principle of bevel wheels
mav be found in M. Hatchette’s work entitled " Traite elementairedesmachines.”
*
C 8.
In this figure, A and B are two wheels whose planes are at right angles with
each other, they are put in communication by means of an endless rope, which
after passing round the horizontal wheel B is conducted by the vertical fixed
pulley to the vertical wheel A. The wheel B may have rectilinear motion along
the bar a b, revolving on its axis at the same time ; in vvhich case the motion
should be considered as belonging to Section 17 ; but if this change of position
of B be prevented, it will then arrange itself in this paragraph. This contrivance
is adopted in our cotton spinning machinery,
H 8.
Let A B and C D be two parallel axes on each of vvhich is placed three
toothed wheels a, b, c, and a', b', c'; the w heels a and a' situated at the
opposite extremities of the two axes, are of equal diameter, the wheels c and c'
vvhich are also situated at the opposite extremities of the axes, are of equal
diameter, b and b' the middle wheels on each of the axes are also of equal di-
ameter ; the wheels of the axis A B are fixed to that axis, but those of the axis
C D are fitted so as to be capable of turning with considerable friction, and
M82
any one or more of these may be firmly attached to the axis (C D) by the arrange-
ments described in the article I 7' or K 7'; this being understood, it will be
evident that we may produce the rotation of the axis C D with the same
velocity as that of the axis A B, by throwing the wheel b into action ; its
velocity will be greater than that of A B, if the wheel a be placed in action;
and if the wheel c is put in action its velocity will be less than that of A B.
I 8.
Let AB, C D and E F represent three parallel axes ; each of whieh carries
two toothed wheels a and b; we will also suppose the moving power to
be applied to the axis AB ; the wheels ab of the axis AB are fixed to that
axis ; the wrheels of the axes CD and EF are set upon them and are at
liberty to revolve with considerable friction, but they may respectively be
attached to their axes by the methods I	K 1'; the wheels a a a are of
equal diameter, and the wheels b b b are also of equal diameter, but the
diameters of the latter are double those of the former. This arrangement
is capable of four different combinations.
1.	If	the two wheels b b of the	axes	CD and	E F are	placed	in action
with the	small wheel a of the axis	A B,	the axes	C D and	E F will revolve
in the same direction, and in a contrary direction to that of the mover, with
the same velocity, whieh will be equal to half that of the mover of the axis A B.
2.	If	the wheels a and a of the axes	C D and	E F are	placed	in action
with the	wheel b of the axis A B,	C D	and E F	will revolve in	the same
direction, and with equal velocities, being double that of the mover.
3.	If the wheel b of the axis C D be placed in action with the wheel
a of the axis a b, and the wheel b of the axis a b with the wheel a
of E F, the axes C D and E F will revolve in the same direction, and the
velocities of the axes AB, C D, and E F, will be respectively as 2, 1 and 4.
4.	If the wheel a of the axis C D be placed in action with the wheel b
of the axis A B, and the wheel a of A B with b of E F, the axes C D and
E F will revolve in the same direction, and the velocities of A B, C D and
E F will be respectively as 2, 4 and 1.83
K 8. Piate 6.
To convert direct and uniform circular motion, into variable circular moiion, tke
velocity of wkich shaU vary by a given law.
IN this figure we have a plan and an elevation of the same parts, each part
being respectively distinguished by the same letter of reference.
If the axis D be required to perform a certam number of re Solutions, as n,
while another, C, performs one revolution, with variable velocity, it will be
evident that any two points of the axes should return to the same positions after
the axe D shall have performed the number of revolutions expressed by n, or the
axis C have performed one revolution. It will follow that these points will
traverse equal spaces during n revolutions of D, or one revolution of C.
In order to simplify the application, we will suppose the two axes C and D
each to perform one revolution in the same time; this example being clearly
understood, ali others will become perfectly easy of comprehension.
Let P Q, and M N represent the axes of two wheels, a b C, a d D, two
toothed segments of unequal radius and equal ares, and arranged on the level
of the line 1, 1 ; (see the elevation) b' e f C, and d' n m D are toothed segments
of equal radius and equal ares, and arranged on the level of the line 2, 2; q C p,
q D r are also two toothed segments respectively equal to the segments a Dd and
ab C, but arranged at the level of the line 3, 3.
It will be seen that by this arrangement the velocities may be varied by fixed
intervals and in any required manner, observing that the points a a, are brought
into contact, when the axis M N has completed the number of revolutions ex-
pressed by n.
This piece of mechanism is somewhat difficult of construction, from the inter-
change of the working parts at each alteration in the velocity, these difficulties
may however be practically lessened, by encreasing the number of the teeth in
the ares, in cases where the effective action of the ares is not produced with
m 284
sufficient facility and certainty, it may be assisted by applying the additional
power of a spring or weight.
The solution of this problem may also be obtained by means of tvvo truncated
cones A and B (figure K/ of the same compartment of piate 6) of equal dimen-
sions placed as represented in the figure, at a small distance from each other,
with their axes parallel, the lesser diameter of A placed upwards, the lesser diameter
of B placed downwards, and the lesser diameter of A, at the same height as the
larver diameter of B. On the convex surface of each of these conical frustums
is formed an helical groove, one extremity of a rope n in is attached to the larger
diameter of B at the point of commencement of the spiral groove of that cone,
and after follovving the entire course of that spiral, it is attached by its other
extremity to the corresponding point on the larger diameter of the cone A.
It is evident that if A revolves in the proper direction with an uniform velocity,
B will revolve also, but with a varying and decreasing velocity, being at first
greater than that of A, in the middle part of its course equal to it, and towards
the end of its course, as much less than A as it was greater at the commencement:
the rope n m, will then be entirely coiled on the surface or groove of A. The
movement cannot be continued in the same direction.
If, instead of cutting spiral grooves on the surfaces of the frustums A and B,
they were left of their original conical figure, and an endless rope substi-
tuted for the rope n m, which shall pass round them, it will be evident that
such a cord may be applied to the cones at any required height, without the
necessity of altering its length. Suppose this endless rope were first placed on
the lower parts of the cones, the uniform rotation of A will communicate a
like motion to B, but the velocity of which will be greater than that of A
in a known ratio, and this movement may be continued at pleasure ; as the
situation of the endless rope is shifted towards the upper part of the frustums,
the ratio of the velocities decreases, when it arrives at the middle of the height,
the velocities become equal, and increase as it approaches the upper ends. The
mechanism is used with great success in England, for the purpose of regulating the
velocities of direct circular motion, particularly in the machinery used in the pot-
teries, and manufactories of porcelain. In these arrangements the endless rope
85
is made to traverse on the cones by a rack movement which is placed between
them and parallel to their axes, and guides the rope. The contrivance is
extremely simple, and produces the required change of velocity in an instanta-
neous manner.
L 8.
The upper figure in this compartment of the plates represents an elevation of
the subject, and the lower a plan ; if we suppose the rnotion of either of the axes
M N, P Q of the preceding figure to be equable, the rnotion of the other may
be either retarded or accelerated equably. This has been effected by M. Roemer
of the Royal Academy of Sciences, in the construction of a wheel whose rnotion
exhibits and explains the unequal velocity of planetary rnotion. See Machines
approuvees par 1’Academie; vol. i. No. 24.
The inventor proposes a conical pinion cut through its whole length, as re-
presented in the upper figure: its teeth work with those of a conical wheel B,
the teeth of which are spirally disposed as a b c in the plan of the figure:
the varying form, dimensions, and position of these teeth as they descend the
spiral, is of course to be determined by the form, dimensions, &c. of thatportion
of the pinion with which they are respectively to act.
M 8.
In this figure, the upper is an elevation of the subject, the lower the plan.
Let A represent a drum wheel; B a truncated cone, the surface of which is cut
into a spiral path from the base to the sumrnit of the frustum, and a b c is a
rope of which the extremity a is attached to the cone ; near to its lesser base,
the rope is coiled upon the spiral, and its other end is attached to the surface of
the drum wheel at C; the equable rotatory rnotion of the druin will produce a
variable rotatory rnotion of the frustum; and if the frustum be made to revolve
with an equable velocity, the rotation of the drum will reciprocally be of variable
velocity.
In w'atch-making, the moveremployed is a spring enclosed in the drum A, which
is called thebarrel or cylinder, the truncated cone B is termed the fusee; the chain,86
which is attached to the barrel and the fusee, is wound up on the latter, whose
property of equalizing the action of the spring is derived from the unequal dia-
meter of its spiral.
Watch-makers are enabled by means of a balance or spring, to suit the fusee
to the action of any given spring.
In the Theatrum Machinarum of Leupold, vol. i, piate 48, we find descrip-
tions of various machines for the purpose of measuring the force of the wind : the
first is simply a sail or vertical frame placed upon a carriage—this is placed
upon a horizontal plane, at one end of which is an horizontal axis carrying a
drum wheel and fusee. A rope attached to the carriage passes over a simple
fixed pulley set at one end of the plane, and after making two or three tums on
the drum wheel, is attached to it; another rope is attached to that point of the
fusee which is nearest to the axis of rotation, and is then stretched by the action
of a weight; the whole is then arranged so that the frame or carriage being
placed close to the edge of the plane or table, the weight whose action produces
the rotation of the axis, shall be in equilibrium with the friction of the carriage
with the plane on which it moves. If the apparatus be now placed so that the
wind shall act at right angles to the sail the carriage will run the entire length
of the plane; but when this movement takes place, the drum makes a rotation
on its axis, and the rope, which sustains the weight, is coiled on the fusee, a
complete equilibrium will therefore take place, and then the radius of the fusee
at that point which is last touched by the rope, will express the force of the wind;
ali the machines shewn by this author are founded on the same principle.
N 8.
A B represents a fixed beam or plank, having a mortice nm cut through it,
and in which is set the axis of a toothed wdieel C; a curved spring is applied
between the centre of this wheel and the end A of the beam, so as to give it
a constant tendency towards the point A; D is an elliptical wheel of which the
periphery is toothed. The equable circular motion of C will communicate to
the wheel D a circular motion of variable velocity. This method involves the
same practical difficulties noticed in the articles K 8 and L 8; the correct action87
of these wheels can in strictness only take place when the teeth are supposed to
be infinitely small; the teeth of the wheels may however be dispensed with, and
an endless rope substituted for them, which has a small degree of elasticity, or
w hich has its tension encreased by means of a weight or spring : paying due at-
tention to the observations made in the article B 8 upon the proper method of
applying them.
O 8.
Is an universal joint which is used for the purpose of changing the direction
of circular motion: it is frequently applied in the adjustments and motions of
astronomical instruments, when it is required to communicate a circular motion
to a distant point, and in a new direction.
A very ingenious application of this movement has been made by Messrs. de
Bettancourt and Bregnet to their telegraph at those points where the line of com-
munication alters its direction; in a memoir presented to the National Institute,
they have shewn that if the rotation of oue of the two axes is equable, that of
the other will be variable ; and the ratio of the velocities will be the same as
that which subsists between the actual subtense of the angles formed on a circle
perpendicular to the axis of the first, by radii which divide the circumference into
acertain number of equal parts, and the apparent subtense of the same angles, to
an observer situated at a great distance, and in a parallel direction to the second
axis. An acquaintance with this property is extremely useful in calculating the
difference of the resistance which takes place in this movement, and especially
when conducted on a large scale; an instance of this occurs in the application of
the principies to the purpose of changing the iuclination of two Archimedian
screws used for draining, and which are worked by the power of wind.
An application of the universal joint has been made to the construciion of a
flatting engine by M. Droz.
The description ofWrighfs sowing or dibbling machine, in which this me-
chanism is employed, may be seen in the Repertory of Arts and Manufactures,
vol. xv, page 369.
The reader may also consuit Technica curiosa sive Mirabilia? Artis of Gaspar
Scholt, 1661, page 664.88
P 8.
Let A B represent an axis the continuity of which is broken by some impene-
trable obstacle, and the separated portions of whicli are required to make their
respectiverotatory movements simultaneously, oras ifcomposedof anentire piece.
To each separate portion A and B of the axis, is fixed a wheel, as E and F,
tliese are of equal diameter: an entire axis N M, is fixed near A B, parallel to it,
and at a distance from it eqnal to the distance of the wheels E and F; upon
this axis are cut the grooves C and D, at right angles to the axis, their distance
is equal to the distance of the wheels E and F upon the axis A B, two endless
ropes or bands pass respectively over the wheels E F, and their corresponding
grooves C and D: the two bands must be disposed in the same manner, that
isto sav, either botli direet, or botli crossed, so that the motion of M N may be
transmilted to A and B in the same direction, which would not be the case if
the bands were arranged dissimilarly, the two portions of A and B would then
move in opposite directions.
Q8.
Practical meclianics employ a variety of methods for regulating the unforeseen
inequalities of the moving power, as well as to protect the machinery, and the
persons employed in its management from the serious accidents to which they are
exposed byabrupt changes in any part of the acting power. The application of
the fusee in the construction of the common watch to the purpose of equalizing
the action of the spring, is familiarly known, as well as the methods adopted to
compensate the variations of length in the pendulum, from the changes of tem-
perature, and to render the vibrations of the balance isochronous: the use of a
fan wheel in clock movements to regulate the action of the moving power is
also well known, and the adoption of the same mechanism in other machinery.
In our article N 7;, we have shewn the methods in general use in steam engines
for regulating the action of the steam. In machinery where human labour is
applied as a first. mover, as for instance, in some of those machines which are99
seen in ali ports and harbours, whether for the purpose of cleansing thcm, or ar
cranes for raising and lowering considerable weights, in case of the rope breaking
the operators would be greatly exposed to danger, but for the expedient usually
adopted of a long beam or spring applied as a curb upon the periphery of
the wheel; the friction thus produced quickly obviates the danger and incon-
venience to be expeeted from such derangement, and compleatiy relieves the
operatore from apprehension of danger, as has been before noticed page 49.
M. Breguet has adopted a piece of mechanism which he intends to effect an
approximating equalization of the aetion of a first mover in pendulum move-
ro en ts, by encreasing the friction in proportion as the moving power is aug-
mented ; this contrivance we consider to be judiciously applicable to other pur-
poses. It consists of three wheels A B C, which are set upon the piate E E E E',
of two pinions, and an arm D; the centre of the movement, whieh is variable
at pleasure, is in E'; the arm carries at the point D a pivot of the wheel B,
and rests upon a cylindrical portion upon the face of the wheel C.
Suppose the wheel A to be moved in the direction of the dart shewn in the
figure, by a variable power, sueh as that of a spring—the aetion of the wheel A
upon the pinion of B will then be as the power operating upon A ; but as the
pinion of B is carried by the piece D, iis tendency is in the direction of B, and
resting with its end on the cylindrical portion of C, the friction of the latter on
its pivot is considerably encreased, which will tend to diminish any excessive aetion
of the wheel C.
R 8.
In this figure we have a plan, and an elevation of the arrangement, in which
as usual, the same parts are respectively marked with the same letters of
reference.
A and B are two wheels of different diameters, as depicted in the figures: they
are each fitted by friction only upon an axis common to both, and which has no
rotatory motion ; and they are arranged at a small distance from each other.
The wheel A is grooved on the edge for the purpose of receiving an endless
rope or band; the wheel B is also grooved on its edge, and has a certain number
jj90
of projecting pieces on its upper surface which compose a series of other wheels
of different diameters, and tlieir edges are also grooved.
Two smaller wheels C, are placed upon an axis situated perpendicular to the
surface of the wheels A and B; the diameter of these wheels is equal to the dif-
ference of the radius of A and B; and they are so arranged upon the axis that
one of them may work with the wheel A, and the other with the wheel B; the
combination and the particular arrangements of this wheel-work is arbitrary,
and will therefore depend on local circumstances and the judgement of the
constructor.
The arm e f terminates in two rings: the commori axis of the wheels A and B
passes through one of these rings with friet ion, and the common axes of the
wheels C also pass through the other ring in the same manner; the axis of the
wheels C is therefore constantly parallel to and equi-distant from the axis of
A and B.
D is a cylinder to which the moving power communicates a direct circular
motion. Two parallel wheels and endless bands transmit that motion to the
wheels A and B, their rotation is in contrary directions, one band passing directly
From D, the other being crossed.
S 8. Piate 11.
We will now suppose the wheels A and B of the last example, to be of equal
diameter; and that for the two wheels C, we substitute a single wheel which
is placed at right angles to the faces of A and B; in short, that A B and C are
bevel wheels, which are arranged and combined as in the figure. The wheel
C is fitted easily on the axis r s e, and the axis D E passes through r s e by a
cylindrical opening for that purpose at s; the wheels A B and C are kept in
their respective positions upon their axes by collars, or similar fittings, which pre-
vent them from sliding upon the axes.
The wheel C has two rotatory motions—one about its axis r s, the other about
the transverse axis D E.
A ring ruem, may be attached to the axis r s e, haying its plane parallel tq
to that of the wheels A and B, as in the figure; the exterior edge of the ring
may be circular or of any required form, or which circumstances may require,
i91
and by tbis means a circular movement may be converted into alternate recti-
linear movement, with any required modification of velocity or direction.
This piece of mechanism is extremely simple of construction, is practicable on
a scale of reduced dimensions, and is capable of numerous useful applications,
of which we shall give selected examples.
SECTION IX.
To convert direct circular motion, of uniform velocity, or which varies by a given
lato, itito alternate circular motion, of velocity either equable, or variable by a
given law, and in the same, or in different directions,
THE arrangements, shewn in the articles E 7, U 7, B 7', E 7', G 7', H 7', I 7',
K 7', L 7', M7', may also be considered as examples of the required conversion.
A 9.
. A is a wheel with waved teeth, and which communicates an alternate circular
movement to the bent lever P S R. The method of constructing these curved
teeth may be seen in the memoir of M. Deparcieux, to the Academy of Sciences,
which we have already mentioned. There is no reciprocal action in this piece
of mechanism.
B 9.
This is a remarkable instance of the preceding example, in which there is
but one wave or curve. An application of it may be found in the Repertory of
Arts and Manufactures, vol. iii, page 220; in the specification of a patent granted
to William Fulton, &c. for a method of working pumps ; and in Les Annales
des Arts et Manufactures, vol. xxii, page 325.
A groove of this figure may be described on the surface of a cylinder,' and if
the extremities of two levers be introduced to it, an alternate motion may then
be transmitted to four pumps at once, under an arrangement by which two of
them shall be elevated while the other two shall be depressed.
n 292
In Leupold’s work—Theatrum Machinarum Hydraulicarum, vol. i, we find
an application of this contrivance to the raising water by means of two buckets.
He places the mechanism shewn in B 9, near the upper extremity of a vertical
axis, which turas constantly in the same direction, by the action of a fall of water
upon the float-boards of an horizontal water wheel. A piece of wood placed ver-
tically in the prolongation of the axis, supports a long horizontal beam, which
presents the precise appearance of a balance, of which the supporting vertical
piece will represent the suspensiori, and the horizontal beam the arms. The beam
carries a bucket at each extremity, and is supported upon the mechanism exhi-
bited in the article B 9, by friction rollers. The rotation of the shaft of the water
wheel will communicate an oscillatory movement to the horizontal arm, and the
two buckets will, by their alternate action, raise the water from a reservoir to an
higher level.
C 9.
In this figure we have an elevation of the subject in the upper figure, and a
plan in the lower figure, with corresponding letters of reference.
The memoir of M. Deparcieux (see A 7) furnishes the methods of describing a
curve a m n p, which is grooved, and fixed to a lever A B which is at liberty
to turn freely upon an axis which passes through its extremity A ; if we suppose
1. That the wheel M has an equable rotatory motion on its centre, 2.—That
the pin p fixed to a point on the surface of the wheel M, shall work in the
groove which forms the curve am n p, this curve may be of such a figure that
the lever A B shall make oscillations which will fulfil one of the following con-
ditions:—1. That the ares described by any point of the bar A B, shall be
described with an equable velocity; 2.—That the velocity shall vary by a given
law; 3.—That it shall not be the arc itself, but rather the chord of that arc
which shall traverse with an equable velocity, or varying by a given law.
The curve described in the present figure, is of a nature to satisfy the first of
these three conditions.
D 9.
We have in this figure also a plan and elevation of the subject, with their cor-
responding letters of reference.
J93
The curve amnp may also be fixed on the surface of the wheel M, and iti
such a manner that the equable circular motion of the wheel M shall commu-
nicate to the lever A B an oscillatory movement which may fulfil one of the three
conditions stated in the foregoing example, by means of a pin p fixed in the
lever, aud which acts in the groove of the curve amnp. The subject of that,
and the preceding article, are capable of various useful applications in the solution
of a great number of curious problems.
If the alternate circular motion of the lever be considered, ali such motions will
be arranged in this place ; but if a grooved bar be fixed on the chord of the de-
scribed arc, the intersection of that groove, with a longitudinal groove made in
the lever, will present an open space in which a point may be inserted which
shall have an alternate rectilinear movement; and in this case, the two motions
C 9 and D 9 will be classed in Section 7. The same will be the case if the
movement be that of a weiglit suspended from the extremity of a bar, by means
of a rope which passes over a fixed pulley. Lastly, if an alternate circular
movement be communicated to the wheel M, the same motions will then be ar-
ranged in the ITth and 19th Sections.
The movement D 9 has been applied to the construction of a watch escape-
ment by M. Volet. (Machines approuvees par l’Aeademie Royale, Vol. vii.
No. 450.)
E 9.
A cylinder A furnished with cams or curved projecting pieces, has a movement
of rotation on its axis, and operates to raise the hammer B, which is suspended
on an axis at C. This motion is too well known to need many illustrative
examples.
F 9.
The upper of these figures is an elevation of the subject, the lower a plan, with
the same letters of reference to each figure.
This gives an inverse solution of the problem in Section IX. A is the lower
extremity of the shaft of a large wheel or fly,‘ on which is fixed the ratchet wheel94
B. CC is a wheel fitted on the shaft of the fly, by its friction, and carries a
click-piece q, which acts upon the ratchet wheel by means of a spring.
The alternate circular motion of the wheel C transmits to the fly and the shaft
A a direct circular motion in the same direction ; but the wheel C will only
act during the half of its oscillation. An application of this motion by White,
may be seen in the report of Messrs. Prony and Molard, adverted to at H 7.
G 9.
This is another application of the movement described in the preceding article,
P Q is a lever having an alternate circular motion, which it communicates to the
W'heel C, by means of the rope abcd e, the proper tension of the rope is pro-
duced by the weight P, or by a spring. The wheel C is fitted on the axis A of
the fly-wheel N, by its friction only ; on the end of the axis of the fly-wheel is
fixed a ratchet wheel shewn in the figure, and in which the click-piece » acts,
the click being fixed on the wheel C. Under this arrangement, the alternate
circular motion of C will cause the fly-wheel N to revolve constantly in the
same direction.
An application of this movement is described in the “ Bibliotheque Britanique,”
vol. vi, article “ Arts,” in an account of a patent granted to T. Bingen, for a
method of producing a rotatory motion, by the action of an alternate movement
in any direction, and which may be afforded by the power of steam or any other
principle. The editor subjoins some observations on fly-wheels.
H 9. Piate 7.
A B is a lever which is capable of an alternate circular motion about the
axis C: cd is an arm which has a free motion on its extremity c; its other
extremity d is fixed to the toothed wheel E, which works with a similar
wheel F set on the axis of the fly-wheel N; on the reverse side of the wheels
E and F, is an arm e f which preserves the constant distance of the wheel E
from the centre of the fly-wheel; the alternate circular movement of the lever
A.B elevates and depresses the wheel F, but this could not take place unless the
i95
wheel F revolved on its centre. According to tlie arrangement of the machine
the actual movement may be either direct or alternate; but the inertia of the
fly-wheel operates to render it direct and nearly equable: a. reciprocal action
takes place, when the machine has commenced its movement. This mechanism
is adopted in steam engine work—a description of it occurs in Prony’s Archi-
tectare Hydraulique, part ii, page 118.
It will be observed, that notwithstanding the two wheels E and F are of the
same diameter, the fly-wheel N makes two revolutions for each oscillation of the
lever, which prevents the necessity of using fly-wheels of the large dimensions
required to produce the same effect in the usual construction,
I 9.
The following is a description of a rotatory motion, for which a patent was
obtained in England by Edmund Cartwright. This rotatory motion is commu-
nicated by steam, and its velocity may be encreased at pleasure, without the
assistance of wheel-work.
A B represents the side elevation of the upper part of the framing which in-
closes the boiler, the cylinder, the fly-wheel, and ali the acting parts of the
engine ; an axis crosses this framing, on which the pulley or wheel C revolves ;
a chain passes over this wheel and is attaclied to the upper end T of the piston
rod; (the wheel C receives an alternate circular motion by the action of the
piston and its counterpoising weight P ;) the wheel C carries a lever handlc D,
which by means of the arm K communicates with the lever F, placed horizon-
tally on the top, or at the side of the boiler. Another axis, w hich may be placed
either above, below or at the side of the first, passes through the fly-wheel G,
and carries at its other extremity a lever handle H, which communicates with
the horizonta! lever F by means of the arm I, as before described of the wheel C
by means of the arm K.
Itis evident that when the wheel C is made to revolve by the action of the
piston T, the arm D which is fixed on its axis, will cause the fly-wheel G to
revolve also, the wheels G and C being connected with the same lever F. If C
therefore be moved alternately in the direction a b and b a by the action of the96
piston, and its counterpoise P ; and if the lever D of tlie wheel C moves in the
same direction, the lever H of the fly-wheel will perform the same alternate
movement, unless it should be (as itought) of such length as that at the termina-
tion of its arc of rotation, it is at liberty to pass beyond it; which in fact, produces
the complete rotation of the fly-wheel.
If the lever D of the wheel C be so disposed, as that when it revolves in any
quantity not exceeding one entire revolution, it shall pass from e to a, by f, or in
the direction traversed by a given point of the wheel C, then D will cause two vi»
brations of the lever for one stroke of the piston, and the fly-wheel G will in the
same time make two revolutions. Further, if the diameter of C be so determined
that it shall complete one revolution and a half for each stroke of the piston, and
retrograde the same quantity, the lever F will receive three vibrations for each
stroke of the piston rod. Lastly, if the wheel C be of such a diameter that it
shall make two direct, and two retrograde revolutions for each stroke of the
piston rod, the lever F will then make four vibrations, and the fly-wheel four
revolutions.
It thus appears that the fly-wheel may revolve with any given velocity, without
the aid of any combination of wheel work.
K 9.
This figure represents the common treadle. If we suppose the lever arm of
the fly-wheel to be connected with the end of the lower lever or treadle, by an
inflexible arm, the relation between the component parts of the treadle, and the
eflfect or action become determinate, whieh, in a certain degree, is not the
case when the arm is flexible; we will suppose the following data:—1. The
length of the lower lever.—2. Its centre of rotation.—3. The value of the arc
which it will describe at each oscillation.—4. The position of the centre of the
fly-wheel with respect to the centre of rotation of the lower lever, the length of
the upper or shorter lever, and that of the longer and inflexible arm, are known
quantities. To determine their value, place the treadle or lower lever in its
two extreme positions, the higher and the lower points of its vibrations, and
draw right lines from the centre of the fly-wheel to theextremity of the treadle in
J97
those two positions. The first of these distances is known, and should be equal
to the difFerence of the length of the inflexible or longer arm, and the upper or
shorter lever; the second, which is also a known quantity, should be equal to
the sum of those lengths; consequently, the length of the longer arm, which
must be more than that of the upper lever, is equal to half the sum of the two
distances betvveen the centre of rotation of the fly-wheel and the extremity of the
treadle, in its two extreme positions ; and the short lever must be equal to half
the difFerence of those distances. If we suppose the angular velocity of the
treadle to be equable, the velocity of the fly-wheel will be variable through its
whole course; but the inequalities of its motion will become less sensible as
the angular measure of the motion of the lower lever or treadle is smaller, and as
the distance between the centre of the fly-wheel, and the centre of rotation of the
treadle is greater.
L 9.
The conversion of an equable circular motion into an alternate circular motion
whose velocity shall be variable according to a given law, is a problern which has
engaged much attention in the fabrication of time keepers. The following
example is selected from the Machines approuvees par 1’Academie, Vol. iv.
No. 267.
“ A clock motion which shews true time, invented bv the curate of St. Cvr.”
“ The annual wheel A carries a curve of equation BCD; upon the face
of this cui’ve is cut a groove parallel to its edges; in the groove, moves a stud E
fixed on the piece E F, and moveable on the point F; the stud is also fixed to
a second piece E G, this is attaclied to the cylinder H, which carries the minute
hand T, so that it follows the variations of the curve more than half the cireum-
ference of the minute dial; which is sufficient to mark the inequalities indicating
the equation.”
Descriptions of other pieces of mechanism for the resolution of the same prob-
lem, may be seen in the following memoirs, contained in the Recueil des
Machines approuvees par 1’Academie des Sciences.
Clock which shews the true time, invented by Le Bon, Vol. iii. No. 146.
o98
A clock rnotion, which shews the true time, by the same author, Vol iv.
No. 235.
Clock, which shews the true time, invented by M. Kriegleissen, Vol. iv. No. 269.
A clock rnotion, which shews the true and mean time, by Thiout, \ol. iv.
No. 278.
An equatorial watch, invented by Dutertre, Vol. vii. No. 453.
An equatorial clock, invented by Ferdinand Berthoud, Vol. vii. No. 48S.
Another clock is described in the seventh volume, No, 495.
M 9.
The following is the mechanism adopted by M. Breguet in an equatorial
clock.
It may be considered as composed of two parts—one of tliem fixed, the other
moveable.
The fixed portion of the arrangement is the square piate A A A A, held by
four screws; it is cut through or grooved in the forni of the curve of equation.
The moveable portion is composed of a piate gg, having its centre of rnotion
in a; it carries a moveable tail-piece which has its centre of rnotion in b; one
of its two extremities c, acts against the edge of the curve ; the other extremity
d, applies to the continuatiori e of an index or needle f, which has the same
centre of rotation as the piate gg. The continuatiori of the index f is pressed
into its action ori the tail d by means of a spring h, the fixed extremity of which
is screwed to one extremity of the piate gg as in the figure; the index J is
fixed on the same axis as the index f and is concentric witli it, or moves on the
same centre of rotation.
The piate gg performs a complete rotation on its centre of rnotion a in one
year; and, as we liave described, carries with it in its course ali the moveable
parts of the machine. It will be conceived that the index J, which is fixed to
the piate g g, might point out the days of the year by being set on a dial divided
into 365 equal parts, and the index might be expected to traverse equal spaces
upon these divisions in eqtral times, which however will not be the case. W hen
the lever c acts on that part of the curve wliich is farthest from the centre, as I,
the index J will be several divisions in advance of the index f; but on the con-91)
trary, when the lever acts on the part M of the curve whicli is nearest to the
centre, the index f will then precede the index J by a certain number of
divisions.
This difference of motion between the two indices is produced by the action
of the lever cbd upon the piate AAAA, and the construction of the curve is
calculated to advance or retard the index f relatively to the index J, by a quantity
of the arc, or a number of divisions equal to the difference between the true and
mean time in minutes, on the day indicated by the index J.
N 9.
The subject of this figure is a ratchet lever: it is the invention of M. de la Ga-
rousse; the description of it is extracted from the account of ” Machines ap-
prouvees par 1’Academie des Sciences/’ Yol. ii, No. 74. In this macliine an
alternate circular motion is converted into direct circular motion, without reci-
procal action.
The hooked arras I L, M N, are moveable on the points I M, and are so
disposed that the lever by its alternate and direct motion, causes one of them to
draw the ratchet wheel constantly towards it, while the other quits the tooth
which it had acted on, and applies itself to another.
The inventor has applied his lever to a macliine for communicating a siraulta-
neous action to four corn mills. Vol. ii, No. 121.
See also figure 1, piate 26 of the first volume of—Theatrum Machinarum de
Leupold.
O 9.
This mechanism is a wheel lever, invented by M. de la Garousse; see Machines
approuvees par 1’Academie, Yol, ii, No, 72. It is a modification of the preceding
contrivance,
The large lever A B has its fulcrum in C; above and below are two sliort
arms D and E, eacli moveable on its centre pin ; and each of them also applies
to one of the spindles of the lantern wheel F.
The alternate circular motion of the great lever produces the direct circular
o 2100
motion of the wheel F, on the spindles of whicli the arms D and E act in rotation.
If a rope were coiled on the axis of the wheel F, a direct rectilinear motion
would be produced, and the arrangement would consequently belong to Sec. 4.
P 9.
In this machine, ab is a kind of pendulum or long lever handle attached to
an horizontal cylinder R, which operates to give it an alternate circular move-
ment; the two click-pieces ou, p k are fixed upon its convex surface and near
its extremities by hinges, and they act upon the opposite teeth of the horizontal
ratchet wheel ST, communicating to it a direct circular movement while the
action of the moving power is uninterrupted.
In Yol. v. No. 209 of Machines approuvees par 1’Academie des Sciences, we
find an application of this movement to the construction of a machine for draw-
ing loads, by M. Alix.
Q 9.
This machine is a modification of the lever of M. de la Garousse, (O 9.) but is
not of equal merit—the power not being constant in its action.
This contrivance has been proposed for raising weights, by M. Henry. See
Machines approuvees par lWcademie, Ypl. iv, No. 264.
Several different arrangements of levers upon this plan may be seen in the
first volume of—L’Architecture Hydraulique de M. Belidor,; and in the—Thea-
trum Machinarum de Leupold.
R 9.
A is a horizontal wheel toothed on its upper face through a little less than one
half of its periphery; B and C are two toothed wheels fixed to the axis d e;
their distance should be equal to the diameter of the w heel A. It is evident that
the toothed portion of the wheel A, which must always be less than its semi-
periphery, will fall into action with the wheels B and C alternately, and commu-
nicate an alternate circular motion to the axis d e.
In Bockler’s work (see E 3 and K3) fig. 109, we find this arrangement applied
to the working of pumps. He first communicates the direct circular motion of101
tlie horizontal shaft of a vertical water wheel to a vertical axis, and then converts
the motion of the vertical axis, into an alternate circular motion upon another
horizontal axis by the contrivanee \ve have described in the present article : and
lastly, the alternate circular motion of that horizontal axis communieates a ver-
tical and alternate rectilinear motion to the piston rods of four pumps: two of
which are made to rise, while the other two descend, and this by the mechanism
described in our article M 17; the pump rods have racks upon thern, and the
horizontal axis has pinions or toothed wheels.
In Ramelli’s work (referred to in our article A T) may be seen an application
of this contrivanee to the action of two pumps.
If the wheels B and C were indented on a portion of their inner faces, and
the wheel A were toothed over its entire periphery, and were placed between the
edaes of the wheels B and C, it will be evident that the direct circular motion
of the axis d e will produce an alternate circular motion on the axis of the
■wheel A.
Bevcl wheels may beintroduced in the arrangements of this piece of mechanism
although we have given no representation of such an application in our figure.
Ramelli, in the work above mentioned, shews several applicatioris of this last
method, which is, in fact, but a modification of the arrangeinent first described
in this article.
OBSERVAT ION S.
In ali mechanical combinations for the measurement of time, the moving
power, or sustaining force communieates a direct rotatory motion to each wheel
of the train. To render this movement uniform, notwithstanding the irregularities
which must necessarily affect all mechanical arrangements of great delicacy,
whether arising- from the moving power—the imperfection of workmanship—the
influence of temperature—or from other accidental sources, the last wheel of the
train, or scape-wheel, has been placed in contact with the regulator; that is to
say—with the pendulum or balance, of the clock or wateh. This regulator
makes an alternate circular motion, which in the present state of perfection of
the art, possesses the property of performing its oscillations in equal times, of102
whatever extent those oscillations may be, or under whatever temperature they
may be performed. These valuable properties are afforded by various methods
of construction, of great ingenuity and intelligence; but the particular consider-
atiori of w hich does not come within our present purpose.
The conununication betvveen the direct circular motion of the scape-wheel,
and the alternate circular motion of the regulator, is effected by a piece of rne-
chanism technieally termed the escapement; its functions are to maintain the
action of the sustainiug force on the regulator against the loss which it suffers at
each vibration from friction and the resistance of the air, and to communicate the
equable action of the regulator to the train-of wheels*.
Ali the known escapements may be arranged in four distinet classes, viz.
1.	The escapements of recoil.
2.	The dead-beat escapements.
3.	The free vibration escapements.
4.	The free vibration, and remontoire escapements.
The recoil escapements are those in which the scape-wheel acts constantly on
the regulator, by its alternate action on two pallets; these are impelled in turn
by the teeth of the wheel, and the regulator continuing its vibration produces
the retrograde motion of the wheel,
The recoil escapements may also be arranged under three distinet heads, viz,
1.	The crown-wheel escapement f.
2.	The anenor or crutcli escapement X-
3.	The double lever escapement
The dead-beat escapements are those in which the teeth of the wheel, after
escaping from the pallet or impelling lever, fall on a circular plane, or on a
portion ofacylinder carried by the regulator, the motion of which continuing,
the tooth remains at rest, There are two descriptions of these escapements, one
* Histoire de la mesure du temps par les Ilorloges, par Bertlioud3 toI. ii? page 303«
+ Essai sur l-horlogerie, par Bertboud3 17863 vol. i3 page 136*
t Idem, vol. i, page 139,
| Idem, vol. i, page 138.103
which is properly the dead-beat escapement, and is adopted in clock-making;
another which is termed the cylinder escapement, and is applied in the construction
of watches.
The free vibration escapement is also a dead-beat escapement, the wheel being
at rest after the impulsion; but the repose of the wheel, in this instance, differs
from that of the escapements above mentioned, in as much as the wheel after its
impulsion, neither comes into contact with, nor rests upon the cylinder carried
by the regulator; but is checked by a piece which is separate from that portion,
so that the regulator completes its vibration freely, without experiencing any
resistance from the escapement.
The free remontoire escapement * differs essentially from ali others, either of
those adopted in clock-making, or those used in the construction of watches:
in ali these escapements, the action of the scape wheel is directed immediately
on the regulator, communicating to it the sustaining force whicli it has itself
received from the train and the mover, without modification; so that this force
caunot be considered as perfectiy equable, from the irregularities of the wheel-
work, the friction of the pivot, and of the sustaining force itself. In the free re-
montoire escapement the scape-wheel does not act directlv on the regulator,
but at each vibration coils aspring into a given position, or to a determined point
of tension; and which at its return, restores to the balance the necessary sus-
taining force: whence it results that the power exerted being equable, and
communicated to the balance, the latter will describe equal ares in equal times.
This invention takes its date from the commencement of the l?th century.
We shall not attempt to detail or describe ali the escapements which have
been invented ; and stili less to constitute ourselves judges of their merit. We
shall confine ourselves to the giving a few examples in each of the four classes
above mentioned : those who may wisli for more extensive information on the
subject, may beneficially consuit the elaborate work of M. Berthoud from whicli
valuable source we extract the following accounts.—
* Hisloire de Ia mesure du tenips^ yol. ii? page- 44.104
S 9.
The crown-wheel escapement.
The scape-wheel 11' receives from Ihe moving power a direct circular motion
in tlie dircction ISI' S',, (so that the perpendicular sides of the ratchet teeth
precede in the progress of the wheel) and it transmits this motion to the levers or
pallets h i, wliich are carried by the verge or vertical axis RK, which is also the
axis of the balance.
The alternate motion, or vibration of the balance is here produecd by the action
of the wheel 11' upon the pallets of the axis of the balance; they are set at an
angleof about 90 degrees with each other, so that vvhen the pallet h is impelled by
one tootli of the wheel, and has escaped, the other pallet i is presented to a tooth
of the wheel diametrically opposite,and is impelled in its turn ; the wheel turning
constantly in the same direction, the balance vibrates on itself, and by its alter-
nate vibratioris regulates the velocity of the wheel I, and consequently the action
of the whole train.
This balance differs materially from those we term regulators, which possess
the property of making isochronous vibratioris.
An improvement of this escapement w as made by M. Huygens in 1675, by the
application of the spring to the balance (a discovery which Leibnitz awards to
M. Huygens.) The intentiori of this alteration was to produce sevcal revo-
lutions of the balance for each vibration ; for which purpose he convcrted the
balance into a toothed wheel, working with a pinion set on the axis of the
balance.
In the works of Rosbery and Bockler, already mentioned in our article K 3,
we find the descriptiori of several mills, in which a weiglit is the movingpower;
and whose action is regulated by a contrivance similar to that here described.
T 9.
The dead-heat escapement for seconds pendulums in clochs, constructed by
Graham.105
This escapement does not materially differ from the recoil anchor escapement
invented by Clement, a clock-maker of London, in 1680.
The piece which forms the escapemeut has also the anchor form; but with this
difference—that the pallets are so constructed as to produce no recoil: this be-
comes what is termed a dead-beat escapement, by means of circular or cylindrical
faces which are formed on the pallets, and correspond with the inclined surfaces
which produce the maintaining power of the pendulum. The Traite de Thiout,
page 93—and 1’Essai sur 1’Horlogerie de Berthoud, No. 1324, may beconsulted
as to the curvature required for the anchor pallets, to produce the isochronous vi-
brations of the pendulum.
T^his dead-beat escapement of Graham’s, when executed with the necessary
care and precision, is stili the most perfect which can bc used for the purpose;
and especially if made with ruby pallets, as is sometimes the case.
The action of this escapement is thus:—The pallet a we may suppose has
escaped, and the other pallet b receives a tooth of the swing-wheel upon its cy-
lindrical portion; the vibration is completed, and the pallet enters the tooth
completely without touching it; the returning vibration is made, and the wheel
remains stationary until the inclined surface of the pallet presents itself to the
point of the tooth—the tooth then acts upon it, the pallet is driven off, and at
its escape the tooth c strikes the cylindrical portion of the pallet a, and is retained
until the inclined surface presents itself; the wheel is then in action, follows the
inclined surface of the pallet, and passing it, gives motion to the pendulum.
U 9.
The dead-beat cylinder escapement for watches, invented by Graham.
F is the scape-wheel ot twelve teeth, upon each of which is fixed a small wedge
or inclined plane i; on the verge or axis of the balance, there is fixed a portion
of a hollow cylinder of steel or other hard material, as is shewn at B in the
figure; the interior diameter of this hollow cylindrical portion is equal to the
length of one tooth of the wheel, and is at liberty to revolve about the tooth
nearly one turn. It will be seen by this description, that when the balance ad-
p106
vances from a, towards b and c, the wheel P is in a quiescent state; and when
the point a arrives at the extremity of the inclined plane i, the action of the
wheel will be thereby transmitted to the balanee, and the inclined plane rests
upon the interior C of the cylinder; the wheel has another interval of repose,
the balanee returns in the opposite direction, again receives the action of the
same inclined plane at its exit at C, and the following tooth applies itself to its
exterior curve in the same manner as the preceding otie, and so on of the rest.
See the description of this escapement, in the Traite d’horlogerie de Lepaute,
printed in 1755, page 171 ; in 1’Essai sur 1’horlogerie par Ferdinand Berthoud,
Paris, 1786, vol. i, page 131; and in the Traite des echappemens par Jodiny
Paris, 175f, page 132.
A 9'.
Dead-beat pin escapement, by M. Amant, clockmaker of Paris.
It is composed of a plane wheel, on which is arranged a circular line of pins.
The pin I quits the pallet A, and the pallet B receives the impulse of the escape-
ment; the vibration continuing, the pallet B falis, and the wheel rests, the
seconds hand of this escapement has therefore no recoil. The vibration is re-
peated, the pin acts upon the inclined plane, restores the movement, and so on.
We here see that in dead-beat escapements as soon as a tooth of the scape-
wheel has effected its impulsion of the balanee, the same tooth rests on a portion
of a cylinder which is carried by the balanee, so that this tooth acts upon the
cylindric portion of that axis during the whole time occupied by the balanee in
completing its vibration. Now, as this cylindrical portion of the axis is of
course contiguous to it, it necessarily foliows that while the balanee completes
its vibration, and the action of the scape-wlieel is thus suspended by the cylin-
dric portion of that axis, the scape-wheel itself will be perfectly quiescent;
that is to say—it w ill never advance nor recede, whence the appellation of this
escapement is that of repose, or dead-beat escapement; but notwithstanding the
apparent advantages of this escapement, its principle of construction renders it
naturally liable to much detrimental influence from oil, friction, and other con-
sequent irregularities, however perfect may be its mechanical exeeution. M.
Berthoud states—that these difficulties or defects in the common dead-beat e9-107
capements, induced him to seek the practical means of remedying them : for
this purpose he arranges the escapement in such a manner that vvhen the wheel
has produced its impulsion, the balance may complete its vibration freely, and
that during that time, the action of the wheel shall not be interrupted by the
balance itself, as in the common dead-beat escapement, but by a detent which
is disengaged by an instantaneous movement, so that the balance may not.
thereby encounter any other resistance or friction than what arises from the dis-
engagement of the detent; and further, that the impulsion of the wheel shall be
transferred to the balance with the least possible quantity of friction, and under
circumstances which shall obviate the necessity of applying oil to the works.
Such were the original ideas of M. Berthoud of the requisite construction for an
escapement, which he denominated a free vibration or detached escapement.
In this escapement the balance makes two vibrations while but one tooth
of the wheel escapes at a time, that is to say—that the balance shall vibrate on
itself, and that the wheel in its escape at the return of the second vibration, shall
restore to the regulator in one vibration, the loss of maintaining power which it
has sustained in two. Thus, during the whole time of one vibration, and the
greater portion of the second, the action of the wheel will remain suspended by
the detent, allowing the balance to vibrate freely.
The invention of the free or detached escapement seems to belong equally to
different artists, who without any inter-communication among themselves, had,
as it should seem, nearly the same ideas of the subject. The persons who thus
seem equally entitled to claim priority of invention are Le Roy, Mudge, and
Ferdinand Berthoud. It appears however, that many years antecedent to this,
J. Dutertre had organized a similar contrivance, but which was not published,
and we are consequently unacquainted with the particulars of its construction.
B 9'.
Free escapement, as invented by Arnold.
C is the scape-wheel of this escapement; D a circular piece set on the axis
of the balauce; t a small projeeting point from the axis; nm a spring having
p 2108
its centre of motion in n; the action of this spring is to press constantly towards
the wheel C, and its progress in that course is checked by the projecting piece
q; a point p also projects upwards from its extremity m. The spring n m carries
a second spring rs of extremely delicate form and action, and which has its point
of snpport in r.
This understood, \ve will imagine the balance to vibrate in the direction indi-
cated by the dart in the figure; the projecting pin t, will then fall into contact
with the extremity s of the fi ner spring rs, which opposing little resistance, will
allow it to pass; but at the returning vibration in the contrary direction, the
spring r s will meet the obstacle p, and instead of bending in the point of sup-
port r, it will cause the first spring n m to bend on the point n, and will conse-
quently allow the escape of a tooth of the wheel C; at this moment another tooth
of C will strike into the indention of the piece D, and restores the loss of power
to the balance. Thus at each double vibration of the balance, the point q of
the spring n m releases a tooth of the wheel C, and the balance receives a new
impulsion.
C 9'.
Free Escapement, by Ferdinand Berthoud.
The description of this escapement is extracted from the inventor’s work—
Histoire de la mesure du temps par les horloges, vol. ii, page 35.
In the figure, A represents the escapement wheel, ab e the detent; the arm a
of the detent suspends the action of the wheel, while the balance makes a free
vibration; the spring d brings back this detent as soon as the pallet c has
thrown off the arm b: at the same instant a tooth of the wheel A acts upon the
cylinder h which is carried by the regulator, and transmits the maintaining
power to the balance; the balance having completed another vibration—returns,
and in its retrograde motion the pallet c meets the end b of the detent; but this
recedes, flying otf from the arm b and towards the centre of the more distant circle
from b, and the spring 1 brings it back to its action when the balance has com-
pleted its vibration ; so that at its return, the pallet c is again presented to the
arm of the detent to disengage the wheel and repeat the impulsion of the balance.109
Haley’s free Remontoire Escapement.
Iu the year 1796 Mi\ Charles Haley, an English watchmaker, obtained a
patent for a free remontoire escapement: a description of whieh is inserted in
the Repertory of Arts and Manufactures, No. xxxiii, page 145. Vol. VI.; and
in the Annales des Arts et Manufactures, Vol. VIII. page 38 ; and M. Berthoud
has extracted an account of it in the seeond volume of his work—" Histoire de
la mesure du temps par les horloges.”
A description of the escapement of Delafons may also be seen in—" Les An-
nales des Arts et Manufactures, Vol. ix, page 69.”
D 9'.
Description of Breguefs Remontoire Escapement for Watches.
This account is extracted from Berthoud’s “ Histoire de la mesure du temps
par les horloges, Vol. ii, page 55.”
A A is a piate of metal upon whieh is fixed the entire movement of the es-
capement.
In order clearly to describe the mechanism of this escapement, it will be more
satisfactory to the reader to consider it under three distinet portions or divisions,
the respective action of whieh will be stated separately, and their relation to each
other afterwards explained.
Part 1. This portion of the arrangement is composed lst of the wheels B B'
and D whieh are fixed to each other. The wheel B B is placed in action with
the moving power by a train of wheels, whieh produce its rotation in the direc-
tion B C B'.
2nd—Of a pinion g whieh drives the wheel BB'; its teeth are equal in
number to so many of those of the wheel B B' whieh are contained in the space
between two following teeth of the wheel D D7. This pinion will therefore at
each of its revolutions be opposite to a tooth of the wheel DD'. On the axis of
the pinion is a fly igh; the branch gi of whieh, is shorter than the other g h,
at the extremity of whieh is a small piece of steel.110
3rd.—Itcontainsa check spring rrF, fixed at the end rr and placed at right
angles to the direction of the fly; at about two thirds of its length from its fixed
end, there projects a piece Y which carries a ruby or other precious stone, or
a piece of tempered steel. In that state of the mechanism which is repre-
sented in the figure, the ruby presses against the extremity h of the fly; and
so performs the office of a stop, which prevents the fly from moving in the direc-
tion in which the pinion g would carry it by the action of the wheel BB'; it
thus suspends the motion of the wheel B B', and consequently the action of the
moving power. But if from any cause the spring rrF is inflected on the side of
the pinion g, at the moment that the stud V, comes opposite to the notch near
the extremity h, the fly escapes, and performs one revolution; and if at the
completion of that revolution the spring rrF has taken its first position, it will
be stopped by the stud V and will pass no further.
Part II.—The second portion ofthe arrangement is composed-----
lst. Of an impelling spring G, curved at its extremity. This spring, as will
be more fully explained hereafter, serves to restore the maintaining power to the
regulator at each oscillation; it carries a projecting piece or catch m, within which
is a small notch, having a ruby projecting from its interior surface. YVben the
impelling spring is inflected by the action of the wheel D D' which comoiunicates
to it the action of the first mover, it is checked by this catch and its stud together
with a piece we shall presently describe.
2nd.—Of a check spring a H, fixed at its extremity a, and upon which is
fastened a very delicate spring N. The spring H carries a ruby p, which enters
into the notch of the catch m, and fixes the spring at its inflection. Another
jewelled stud placed at its extremity s holds the spring N, so that the end of the
spring, pressed from right to left offers but little resistance; and pressed from left
to right, it throws ali its effort upon the stud s, and inflecting the spring H dis-
engages the jevvel p from the cavity of the catch m.
3rd.—The pieces K and b are carried by the upper extremity of the axis of the
balance, and are so placed as to forai an angle of 90 degrees between them.
When the balance vibrates from right to left, or in the direction b K, the piece
K inflects the spring, and passes beyond it; and the piece b being situated111
above the plane of the wheel B B' and below that of the spring H, the vibration
from right to left is perfonned freely, and without any other obstacle than the
flexion of the spring N. But when the balance afterwards vibrates in the con-
trary direction from left to right, the piece K presses the spring N against the
stud s, the spring H is inflected, the stud p is disengaged from the catch m*
and the spring G, left to its own action, operates as we shall presently describe.
On preserving and communicating the sustaining Power.
The action of the arrangements for preserving and communicating the sus-
taining power, will be clearly understood from the preceding description. At
the instant the stud p of the spring H is disengaged from the catch m of the
spring G, and G is released, the straight side of the piece b is at right angles
to the direction of the extrernity q of the spring, which strikes it, and imparis
to the balance the power necessary to enable it to complete its vibration : im-
mediately after this first percussion, the same extrernity q strikes the end F of
the spring Frr, inflects it and drives the stud V opposite to a notch in the
fly ih, which is thus released ; and the movihg power which acts on the wheel
BB' and thus on the pinion will cause it to perform one revolution, at the
completion of which, the spring Frr being again in its first position, it is
checked by the stud V; but during this revolution, a tooth of the wheel DIV
has pressed against the projeetion n (which is shewn near the end q of the spring
G ) and has forced it back ; and this action continuing according to the relation
of the wlieels B and D, until the stud p of the spring H is again engaged
in the catch m ; every part of the machine will then be in the situation repre-
sented in the figure, and the action be repeated as before.
E 9'
This piece of mechanism is a remontoire escapement for elocks, and is invented
by M. Breguet.
A is the last mover, and moves from right to left in the direction of the dart
shovvn in the figure.112
B,	a wheel of six curved teeth, set on the axis of the wheel A; but at its op-
posite extremity.
C,	a pinion acting with the wheel A, and performing six revolutions for one
revolution of the wheel A.
D,	A fly-wheel set on the arbor of the pinion and fixed there by its friction
only; by the operation of a small spring, it is allowed to continue its motion,
when the pinion is suddenly checked.
E,	a small vane, or cross-piece of steel fixed on the arbor of the-pinion C, and
resting against the stop or check-pieee F.
F,	the above-mentioned check-pieee, turning on the pivot V.
G,	an arbor which carries three pieces of considerable importance in the ar-
rangement:—1. The piece c, which has on one side the curved tail-piece or
tooth d, and on the opposite side two ratchet teeth e f: the first of these operates
to stop the motion of the arbor by means of the check-pieee H, and the second,
to impel the pendulum when the arbor is entirely free;—2. A pin, or small roller
g, fixed in the piece c for the purpose of raising the check-piece F;—3. A small
weight h, whose distance from the axis may be varied by means of a screw ad-
justment, in order to regulate the impelling force which acts on the pendulum,
according to the arc of oscillation required to be described.
H,	a check-pieee which turns freely on its centre, which is fixed to the case of
the wheel-work.
11, the bob of the pendulum, suspended to the upper extremity.
h L, a piate of copper fixed to the bob of the pendulum.
M,	a small and very light lever, which at one end turns on the pivot i, and at
the other presses on the pin 1; the extremity furthest from the pivot carries a
projecting edge-piece m, which disengages the piece H, and the arbor G.
N,	an edge-piece, on which the pendulum receives its impulsion. Its pro-
jeetion or elevation above the plane of the piate L L should be such as will allow
it to pass freely behind the piece H, and having a portion of its thickness to
engage with the piece C; its lower part should glance upon the tooth f at its
movement, but without any actual contact.
The moving powcr turns the wheel A, the cross-piece E will be stopped by113
the piece P: if we suppose the bob of the pendulum to oscillate from right to
leftj, the projecting piece m of the lever M will be in contact with the check-
piece H, and will disengage the tooth e, while the piece N is presented to the
impelling tooth f. The arbor G is then completely free, and the action of the
weight h, as well as the weight of the tooth d, gives it a tendency to turn from
right to left; and its motion being quicker than that of the pendulum, it arrivesat
the piece N, and impels it, the tooth f rising in its progress. The arbor G
continuing its motion, the pin g comes in contact with the lail of the check F,
and leaves the fly D free: the tooth d being at the same time opposite to
the tooth f. Therefore, while the fly performs one revolution, the tooth p acting
upon the tooth d brings the arbor G to its first position; the piece f presents
itself to check the fly, and the piece H acts upon the notch e to check the arbor
G. The pendulum in its motion from left to right experiences no opposition
but from the head of the piece II to which the edge m applies; but the ter-
mination of these pieces being similarly sloped or inclined, the lever M raises
itself, and afterwards*falls to its first position.
This method of preserving the sustaining power of a pendulum in its oscilla-
tions, we consider to be the most perfect of any at present known.
F9'. Piate H.
In our article I 7' we have observed that in weaving machinery, the shuttle
frame is required to traverse the arc ab (F 9') with an alternate circular motion,
the axis of rotation being in C; that its velocity should not be equable, but
decreasing as it approaches the extremity a of the arc a b nearest to the large
roller, and accelerated as it approaches the other extremity; and that this alter-
nate circular motion subjected to these conditions, is communicated to the shuttle
frame by the direct and equable circular motion of an axle d, which is driven
by any moving power.
This problern may be resolved with ali desirable precision and facility, by the
methods already explained; the following method by approximation has been
used in England, and we have also seen its application in Paris, in the manu-
factory of M. Cala, an eminent constructor of spinning machinery.
Q114
Let d e represent the crank arm of the axis of rotation d, its length equal to
half the chord of the arc ab; efg a metal rod suspended in the point f to a
second rod f h, which turns upon the point h. While the point e of the crank
proceeds from e to e, from 1 to m, and from m to n, the point f of the rod h f
passes from i to f, from f to s, and from s to k; and consequently the distance
k i will be equal to the distance n 1. The shuttle frame being required to tra-
verse the arc ab in the same interval, the distance ai is divided into two parts
ir and ra, the portion fg of the rod efg is taken equal to r i, and a third rod
gp equal in length to ar, is placed as in the figure, so that its extremities may
turn freely on the points g and p of the rod efg and the line c p of the shuttle
frame; and the shuttle frame will traverse the arc a b with a velocity the varia-
tions of which will depend on the relative proportions of fg and gp; these dis-
tances will be easily arranged by a few trials.
G 9'.
Let A B represent a horizontal shaft, which receives an alternate circular
motion from the moving power, n and m two ratchet wheels fixed upon the shaft
so that their teeth are reversed with respect to each other; C, D and E three
toothed bevel wheels, of which C and D are of equal diameter; they are held
on the shaft A B by friction only ; they carry the two click pieces p and q, and
they work with the third wheel E, the axis of which is properly supported. The
shaft A B, by its alternate circular motion, acts on the wheels C and D alter-
nately, and soon acquire a direct circular motion; and, as this must take
place in opposite directions, the wheel E will turn constantly in the same direc-
tion; and thus, the alternate circular motion of an axis or wheel, may be converted
into the direct circular motion of anotlier wheel, the direction of the second axis
being at right angles to that of the first, or the plane of the second wheel being
at right angles to that of the first.
H 9'.
The conversion of a direct circular motion, into an alternate circular motion,
by a method sufficiently simple for practical purposes, and which will allow the115
alternations to be regulated at pleasure, is a problem of universal interest with
mechanics and artists of every description.
In our articles L 7', (Piate 4), and M 7', (Piate 5), we have given tvvo ex-
amples of the conversion of direct circular motion into alternate rectilinear motion,
by the action of a counterpoising weight, which acts alternately on the opposite
sides of a vertical line passing through the axis of rotation of the arm; the alter-
nate changes of position, taken by the weight alternates the action of an arrange-
ment of wheel-work, which converts the rotatory motion of a spindle into an
alternate motion, as in the case of the axis E F in the figure L 77, and the two
cylinders F and G in the figure M 7'; the alternate circular motion so produced
is afterwards converted into alternate rectilinear motion. In these two examples
we see the methods by which the change of position of the counterpoise is efiected;
and which are calculated for the particular purposes of these machines; but in
general whenever a counterpoising weight.is adopted for the conversion of direct
circular motion into alternate circular, the periods of the alternation may be re-
gulated either by some simple combination of wheel-work, or by the arrange-
ments D3 Piate 1, and S 8 Piate 11, which will be found of universal ap-
plication.
Let MN, figure H9', Piate 11, represent an axis corresponding with E F in
the figure L?7, Piate 4, or to one of the cylinders F or G in the figure M 7',
Piate 5; P, the counterpoising weight; n o, the axis of rotation of the vertical
arm on which the counterpoise is supported; q o an arm placed at right angles
to the vertical arm and the axis no; esr, the axis of the machine S 8 Piate 11,
placed as in the figure ; it will now be perfectly easy, as has been already ex-
plained, to cause the arm r s to perform only one revolution about the axis D E,
while the axis M N shall make n revolutions at pleasure. We will now suppose
that the axis rs be raised from the lower towards the upper part of the figure,
and on its arriving there, the counterpoising weight P will be situated in
the vertical line which passes through no; it will now fall towards the point p' ;
the rotation of the axis M N will be changed; the axis s r will also return in the
opposite direction, \vill meet the arm oq at the upper part of the figure, will
Q 2116
retura it from the upper to the lower part, and cause the weight P to move
tovvard p"; and so on.
I 9'.
In this figure we have a plan, and an elevation of the subject:—the figure on
the right being the elevation, that on the left, the plan. The same parts of the
machine has in each figure the same letters of reference respectively.
The mechanism shewn at D 3, Piate 1, may be employed here for the same
purposes, as follows:—
That arrangemeut may be placed as in the present figure, the axis A B is
terminated by a square arm gh which is fitted by its friction into an aperture
cut in the centre of the pulley G; this pulley is supported by a collar, or in any
sufficiently substantial way, which willnot impede the rotatory motion ; the move-
able nut M' carries a forked piece or double-armed lever iklm; an endless
rope passes round the axis M N and the pulley G, by means of the fixed
pulley H.
The circular motion of the axis M N is communicated to the pulley G, and
consequently to the axis A B ; and this axis in its rotation is at liberty to rise or
fall freely; if we suppose the nut M' to rise, the lower branch m 1 of the forked
piece iklm will come into contact. with the lever oq of the counterpoise P,
and cause the weight to fall towardsthe right hand ; (see the plan) the arbor M N
at the same time will move in the opposite direction; the nut M will descend,
and the upper branch i k of the forked piece comes into contact with the lever o q,
and by its action carry the weight P over and allow it to fall on the other side,
io the period proposed; and so on. An arrangement of pulleys of different dia-
ameters may be substituted for the pulley G, as is done in the toothed wheel B
of the mechanism S 8, Piate 11 ; the periods of intermission of the alternate
circular motion, may by this means be varied at pleasure.
The mechanism shewn in our subject P 3, Piate 10, may be also used as an
auxiliary method of resolving this problem.
K 9'.
This figure comprehends a plan and two elevations for the illustration of the117
subject, in which as usual, the same letters of reference are respectively affixed to
the same parts.
The mechanism shewn in our fisure S 8, Piate 11, also applies directly to the
general solution of this problem, without the necessity of a counterpoising weight;
thus, let A B and C D represent two axes, each of which carriesa pulley, a of
one of them, a' of the other; and also a toothed wheel on each, b and b'. An
endless rope or band presses crosswise over the pullies a and a', and produces
their simultaneous circular motion, in opposite directions. Let E P represent
another axis carrying a toothed wheel c, this axis is at liberty to alter its distance
from the axes A B and C D, or to move between them approaehing one of them,
while it recedes from the other, its pivots being let into the oblong aperture d d' •
it thus operates to carry the wheel c into working contact with the wheels b
and b7 alternately, and so to convert the direct circular motion of the axes A B
and C D into alternate circular motion.
An attentive inspection of the several figures of this subject, with reference to
the description already given in our article S 8 will give a complete idea of this
mechanism. In the two upper figures of K 9', or the pians, the curves efgh,
e' f' g' h' will be observed; each of which is composed of two parts, the first
portion of each is circular and they are respectively marked efg, and e'g';
these portions support the axis E F alternately in its bearings towards C D and
AB, the other portions gh and g'h' operate to communicate the shifting move-
ment to the axis E F.
SECTION X
To convert direct circular motion, of uniform velocily, or which varies by a given
law, into that of a curve of given species, direct and continuous, of velocily
similar to that of the moving power, either equable, or variable by a given
law, and in the same or in different planes of direction.
A 10. Piate &.
First general Solution of the Problem.
Let F represent the given curve; and let it be required to trace or describe it118
meclianically by a pencil or other instrument upon the surface P Q by means
of the direct circular motion of the whcel D. For tliis purpose three wheels
A, B, C must be taken of suitable diameter, and arranged as shevvn in the figure,
and wliich shall receive their motion through the operation, and by their con-
nection with the wheel D ; m n, p q are two rulers or bars, which are at liberty
to traverse to and fro in the clips or directing grooves a,b, c, d. They are termi-
nated in m and q by two rulers or bars r s, tu, each having a straight groove
or chaunel cut through it. The pencil or instrument with which the curve is to
be traced is to be fixed at the point of intersection of tliese two grooves. A
certain number of points are assumed at pleasure upon the given curve, and the
number of them for the reasons explained in the article A 7, should be encreased
at those points of the curve at which the most abrupt changes of direction take
place. The proper curves thus obtained must be traced, and placed on the
surfaces A and C in relief, and so arranged tliat the extremities n and p of the
tracing points shall be pressed into constant contact with them by means of
springs or other suitable contrivances; and the points of intersection of the
grooves or the positions of the pencil, will tlien traverse the previously deter-
mined points.
From this mechanism miglit easily be devised a mechanical method of ex-
plaining the laws of the resolution of forces, and the motion of projectiles in a
resisting medium or otherwise; if such methods might be considered of sufficient
importance to warrant ourthus encreasing the number of our scientific apparatus
and instruments, which it must be confessed seem already to be more numerous
than the legitimate purposes of Science properly require.
B 10.
The general solution which we have given of this problem in the preceding
article, is the only solution which accords with the plan of our analytical table,
in which the principal object is to shew the transformation of one movement to
another. But in the practical arts, it is essential not merely that the desired
resuit be produced, but that it should unite simplicity of arrangement, with a
facility of construction, and which shall be effective and suited to the babits and119
comprehension of workmen. For the due performance of these conditions, the
movements should be judiciously arranged with respect to the different parts of
the machine, and as the distribution of parts will be arbitrary, the same end may
therefore be produced in various different ways. It is the business of an accom-
plished mechanist to calculate ali the practicable eombinations which may be
made with the component parts of a given machine, and the required number of
movements, and to adopt the most simple and effective.
The object of the problem we are now considering, is not so much to produce
the curvilinear motion of a given point, or tool of any description, as to describe
that curve on a given plane surface. To this end, the surface P Q is attached
to the extremity of the artn p q; this surface, which was previously fixed, will
thereby receive an alternate rectilinear motion ; having fixed the pencil or cutting
tool to the end m of the other arm m n, corresponding curves will be traced on
the surfaees A and C, and a machine will thus be obtained which we consider to
possess much novelty and usefulness.
Second general Solution of the Problem.
The principal points of a given curve may also be governed by angular co-
ordinates. These curves are of two descriptions:—1. Continuous or returning
curves, in the interior of which a point may be determined—such as that ali
right lines passing through it, shall pass through but two points in that curve.
2. Similar curves in the interior of which no point can be assumed which pos-
sesses that property.
The eurves of the first-mentioned description may be easily described by a
direct circular motion, thus: Let ABD, (figure «, piate 10.) represent the
given curve, and let any point C be taken within it for the centre of rotation of
the circular movemcnt of the bar P Q, which revolves in the same direction, while
the bar T O slides upon PQ. During the motion of the point O over the given
curve, the end T traces another abd, and reciprocally, the assumed length of
the bar OT being arbitrary, the bar OT', might have been taken instead of
it, in which case the curve a' b' d' would have been produced, answering the
proposed conditions of the problem.
The curves of the second description involve some difficulty. Let A, B, D,
(figure/3, piate 10.) represent the given curve: there does not appear on the120
first consideration any general solution of this problem, in whatever position
the point C may be assumed ; for the circular movement of the bar P Q being
direct, while the bar OT follows its direction the solution of this problem thus
becomes impossible; a little further consideration however will i-ndicate the
method of proceeding.
Suppose that the line O T (figure i, piate 10.) instead of being placed in the
direction P Q, shall make a constant angle with it as COT ; if during the pas-
sage of the arm P Q to the position P' Q', the point O approaches the centre
and arrives at O', the point T will pass to T', having experienced a retro-
grade movement relatively to the movement of P Q. This will sufficiently
point out the practicability of a general solution of the problem.
A detail of ali the operations connected w ith this subject, would lead us into
considerations essentially distinet from the general object of our wrork. We shall
therefore pass on to our usual descriptive mode of explaining the practical ap-
plications of the problem.
Having shewn the methods of tracing curves formed by a circular, and an al-
ternate rcctilinear motion, we will now suppose the surface on whicli the curve is
to be traced, to have a circular movement while the line T O has an alternate
rectilinear motion, so that the whole line, or only the point O of it shall be
constantly found in the direction of a radius of the circle described by a given
point of the revolving surface.
In this point of vievv, we find this problem give rise to a practical art of great
elegance and utility, viz.—The branch of ornamental turning, which is termed
—rose engine turning. Mueh practical information in this art may be obtained
from “ le Manuel des tourneur de Bergeron,” and the French Encyclopedie.”
In the Memoirs of the French Academy of Sciences for the year 1734 we find
two Memoirs on this subject by M. de la Condamine; the first given at page 216,
is entitled “ Recherches sur le tour ; Description et usage d’une Machine qui
imite le Mouvement du tour*.
* M. de la Condamine in his second Memoir, gives the solution of some problems analogous to those
general ones whose solution we have here pointed out; he however considers them in a different point
of view.121
We have introduced the simple method shevvn at CIO of our piate 8, as an
effective substitute for M de la Condamine’s machine. It is cornposed of an
auxiliary wheel A, which drives two other wheels B and C, which in the latter
are placed on the same axis. The rosette D is affixed to the first wheel B ; the
pin m n, which is attached to the sliding bar P Q, presses upon its edge by
means of a spring a b acting on the end p of the bar. At the point q of the
moveable arm p q is set a point or pencil which may be placed at pleasure in
any part of a circle of paper placed on the surface C.
The practical use of this machine is, as M. de la Condamine observes, to de-
termine the variety of figures which may be described by the tool, from the
same rosette, a matter extremely easy to accomplish. We shall refer to his
memoir for a detailed account of the various forms to be obtained by changing
the rosette, or varying the position of the tool or pencil.
In actual practice, those rosettes will be found most commodious, the lines of
which form the most obtuse angles; the motion of the pin mn is thus rendered
more uniformly steady.
M. de la Condamine observes, that the second practical use of the machine, is
to determine the proper species of rosette suitable to any given design.
He says, “ Having properly determined the place of the tracing point,
“ and secured it in the required position, it only remains to set it by hand
(t to the design for which the rosette is required; and the other extremity of the
“ bar which in the common use of the machine, is pressed upon the edge of the
“ rosette, will trace the rosette required. For the present purpose therefore, a
plane surface of paper or pasteboard is substituted on the wheel B for the
“ model of the rosette before placed there, and the end m of the point m n,
u which in the former case applied itself on the outline of the rosette, will novr
" carry a pencil which will describe the outline of the figure required,”
D 10,
The second memoir of M. de la Condamine, page 303, of the Memoirs of the
Academy, is entitled—“ Recherches sur le tour, second memoire. Examen de
R122
la nature des courbes qui peuvent se tracer par les mouvevnens du tour.” He
gives the Solutions of the two following problems.
Problem 1.—The outline of any rosette being given, with the respeetive po-
sitions of the centres of the tracing point, and the cutting tool, in the same plane,
to determine on that plane every point of the corresponding design.
2.—Any design or outline being given, with the position of the centres of the
tracing point or of the cutting tool, to determine on the same plane, the outline
of a corresponding rosette.
The solution of these problems is so simple, that we do not consider it neces-
sary to enter into any detailed explanatiori of them. For further particulars on
the subject, the memoir itself may be consulted.
M. de la Condamine afterwards gives the description of the instrument.
shewn at D 10, whicli, he observes, affords a ready and correct mode of
determining at once, and of describing by a direct motion, rosettes for the pro_
duction of every possible outline of a given design ; or reciprocally, to trace every
possible design to be obtained from any given rosette, and this without the ne-
cessity of wrought models, as in the machine described in the first memoir.—
ABCD is a bar or rule of three inches in length, liaving a longitudinal groove;
the portion A B is perforated with several screw apertures, in any of which the
point B may be screwed so as to vary its distance from the end A as may be
required; the bar ABCD is held or supported by the clips E G of a second
bar, which is also perforated with a longitudinal groove; the first bar has a
sliding motion through the second, which carries a small hollow spring cylinder
or barrel L, the action of which tends constantly to draw the longer bar in the
direction D A, being attached to it by the band D ; the lower bar also carries
a second point N, which consequently tends continually towards the centre P,
by the action of the spring; the centre is determined by a third point P, which
passes through both bars, and is fixed to the lower bar E G, at any required
point, by the nut z. The instrument is applied in the following manner :
Let the outline of the profile head at T, be the figure for which a suitable
rosette is required ; having first cut this profile accurately in thick pasteboard, it
is glued or otherwise firmly attached to a second surface of th§ same material123
R S, a point T is assumed at pleasure for a centre, within the outline of the
subject; the tvvo cards are then perforated in the point T, and they are together
fastened down on a plane surface, passing the point P through the perforation;
after which the point N is placed in contact with any part of the outline; the
whole instrument is then turned by hand on its centre of rotation P, keeping
the point N in constant contact with the outline of the subject, or in some cases,
it may be preferable to turn the pasteboard on its centre of rotation with one
hand, while the instrument is held firm with the other, attention being paid at
the same time to the accurate and uniform contact of the point N with the con-
tour of the subject.
In both these cases, the point B bearing on the surface of the large pasteboard
RS will describe the line V X, which is the contour of the required rosette;
the point N drawn continually towards the centre P by the action of the spring
L, and its progress in that direction restrained by the relief or thickness of the
subject, will follow its outline with great facility and correctness so long as it
does not lie in the direction of a right line drawn from the centre, which must
be attended to, and avoided as much as possible in determining the point within
the figure for the centre of rotation of the instrument. If in any instance this
cannot be entirely avoided, as in the present subject where the lines which
depict the lower portions of the nose and the chin lie in the objected direction,
and that therefore the tracing point N cannot have its requisite bearing on the
edge of the subject, but slides upon it, the action must be carefully assisted by
the hand; this inconvenience may also be avoided in a great degree by turning
the surface in an opposite direction *. Thus, in this instance the tracing point
will not move up from the nostril of the figure towards the extremity of the nose,
without the assistance of the hand, but will by the last-mentioned method slide
* The author’s directions in these respects should however be followed with considerable caution: it
appears to us, that under the circumstances stated, the requisite assistance cannot be supplied either by
the manual adjustment, or the reversed rotation he recommends, but that the required correction must
be sought by placing the point B out of the direction A D in a suitable manner, so as to avoid the ob-
stacles in question; which may generally be accomplished with practice and attention.
R 2124
easily over that portion of the outline, and will be drawn baek again by the
action of the spring. It must be observed, that in changing the centre P, or
separating the two points B and N in a greater or less degree, different out-
lines will be produced, of which those will be chosen for the model which have
the most easy and flowing curvature, and which are the most practicable in the
subsequent operation of turning. It will be proper to verify this process of
production of the curve, before it is cut, by a process of rcversal, that is to sav,
by carrying a tracing point round the curve produced, and observing if the
point N correctly retraces the original outline of the subject.
In this instrument we have supposed the tracer, the centre, and the cutting
tool to be situated in a right line, that arrangement being at once the most
simple and the most commodious in praefice. The effect of oblique positions
may be easily obtained, by affixing a small arm moveable on a stud or centre pin
at the extremity A of the bar A D, to set the point B which describes the curve
of the rosette out of the alignment with the centre of the point which traees the
subject, and to set it at any reqnired angle with that alignment.
In a descriptive work entitled “ Traite des Instrumens de Mathematiques et
Mechaniques,” by Jaques de Besson, printed at Lyons in 1579 in folio, page 172,
we find accounts of several constructions of compasses for describing rectilinear,
curvilinear, elliptical, and spiral figures. The construction of ali these instru-
ments is founded on the principle of setting a rosette on one of the legs of a
pair of plain compasses, which remains fixed, while the other is at liberty to
make its rotation with the tracing point: ali which methods may be considered
as in fact so many varieties of the simple turning engine. One of these may be
particularly remarked for its simplicity of construction, in which, instead of an
elliptical rosette, a moveable circle is so adapted that its inclination may be altered
at pleasure, and it is also capable of describing any required ellipsis with the
same rosette.
In Yol. VII, No. 455 of “ Machines approuvees par 1’Academie Royale des
Sciences,” we find the description of a pair of compasses for describing spiral
lines, by M. de Thilieres. It is observed at the close of the memoir, that the
second addition of the inventor was detailed in a memoir transmitted to the Aca-
demy in August 1745 for a note in the history of 1742.125
The little instrument for describing ellipses shewn at Figure 8, Piate 12, is
remarkable for its extreme simplicity.
A circular piate either of metal, wood, or any material of sufficient firmness of
texture, and of any diameter, has tvvo grooves n n and m m, formed on its surface
at right angles to eacli other, tlie grooves are of dove-tail consti*uction, and two
sliding pieces B and C of corresponding form are placed in them one in each,
and are at liberty to move back and forward in them, with a small degree of fric-
tion ; from the upper side of each of these pieces there projects a small point or
cylinder, these points fit into cylindrical holesdrilled in the under side oftheruler
or bar B D, one of them at the extremity B, the other at some distance from the
first, along the bar. A pencil or point of any sort, is then held firmly to any part
of the bar, and the bar being turned about on the two centres of rotation, which
are thus both in motion at once, the pencil will describe an ellipse, the excentri-
city of which may be varied at pleasure.
Descriptions of two ellipsographs of much inerit are given in the Bulletin de
la Societe d Encouragement, Vol. xvi, for 1817, page 13; and a description of
an ellipsograph by Mr. William Cubitt, will be found in the Transactions of the
Soeiety of Arts, &c. of London, Vol. xxxiv. for 1817, page 131.
E 10. Piate 8.
Let A, N, B, C, represent a train of toothed wheels, whose ctiameters are res-
pectively as thenumbers 2, 1, 2 and 4; let a'b' represent a bar, whose extremity
a' may be successively fixed to the points 0, 1 and 2 of the wheel A, and ad-
justed also to contaet with the points a c of N, 0 and 1 of B. These points
being so placed that they may be in a right line in one position of the train, every
point of the bar a' b' will move in one curve themselves, and will describe another
on the revolving surface below it.
These curves assume fornis which merit an attentive consideration, and are
of much importance in the arts. It w ill be evident that they may be produced
in an infinite variety, by the various combinations which may be made from the
original places of the points 0, 1 and 2 of the wheel A, a, c of the wheel N, 0 and
1 of the wheel B, and other points taken out of the direction of the bar a' b'.126
The ratio «f the diameters of the wheels, and tlie number of them will
also give rise to new varieties in the character of the curves. This machine will
be considered as a contrivance which may be usefully adopted under particular
circumstances, but the curves it produces may also be described by the preceding
movements A 10, B 10, C 10, D 10.
F 10.
Problem.—To describe a continuous spiral on the convex surface of a given
cylinder.
It will be recollected tliat. this is in fact the process of describing the helix of a
screw of a given diameter.
Let A B represent a fixed axis; to which is firmly attached the cylinder C, on
the convex surface of which it is i*equired to describe the spiral: and the toothed
wheel D. M L K N is a frame liaving a rotatory motion on the fixed axis AB;
between the arms L M, K N, is fixed the axis F G, which has a movement of
rotation on itself, and carries a toothed wheel E, which drives the wheel D; and
also a male screw HI witli its nut P: the nut carries an arm O P at right angles
to the axis of the screw; the extremity O of this arm moves in a groove which
extends longitudinally tlirough the extent of the bar L K of the frame, and at
the other extremity carries a pencil, or cutting tool.
Method of using the Machine.
Let the radius of the wheel E be called a, that of the wheel D be called $,
and the thread of the screw cut on the cylinder HI be called J. If now the
frame M L K N be made to describe one revolution about the axis A B, the
wheel E and consequently the cylinder H I will in the same time describe a
B
portion of one revolution about the axis F G equal to -, and the pencil, or
cutting tool, will in the same time traverse a distance equal to - which will re-
present the quantity measuring the thread of the required screw, or the quantity
of one revolution of the helix to be described on the cylinder C. The value of
this quantity will of course be variable at pleasure, by suitable alterations in the
relation of « to /3, or that of J, by the introduction of different guiding screws.127
It has already been noticed (in our article C 3) that, when the nut is fixed,
and the screw is made to revolve, the movement will be compounded of a rota-
tory motion and one of conversion. This compound movement is precisely that
which is required for tracing this helical line; and it consequently affords the
solution of the stated problem. The movement has been frequently applied in
the construction of pendulum clocks and clepsydrae, and of hygrometers. In
these several machines or instruments the helical line is described on the convex
surface of a cylindrical column, and so becomes the scale on which the progress
of its action is indicated.
An hygrometer on this construction is described in Leupold’s " Theatre uni-
versel de la Statique,” 1726, piate 16.
In this instrument of Leupold’s the hygrometric action is supposed to be im-
mediately directed against a small rack ab, (see our piate 12, figure 9) thus
producing in it an alternate rectilinear motion of small extent; the axle A
carries a toothed wheel B, and a pinion C ; it is so arranged that the pinion is
driven by the action of the rack, whose alternate rectilinear motion is thus con-
verted into alternate circular; the sensible effect of this motion will be encreased
as the diameter of the wheel B exceeds that of the pinion C. The axis n m
carries the horizontal circular piate pq, which indicates by its index s the
hygrometric gradations of the instrument, or the hour, on a properly divided
helical line which may be traced upon the convex surface of the cylindrical
column. The axis nm is composed of two portions essentially distinet: one of
them n r is a male screw working in the fixed nut F; the other r m is a square
bar which slides with some degree of friction in a Socket or aperture of the same
form, in the centre of the toothed wheel tu; this wheel is driven by the wheel B;
it is supported by the flanch piece xx, which rests on the cross framing DE.
The alternate circular movement of the wheel B will be transmitted to the wheel
tu; and the motion of the axis n m, and the index s, will consequently be a
compound alternate motion, as the subject requires.
G10. Piate 8.
This figure consists of a plan, and a side elevation in distinet arrangement,
with the same letters of reference as usual.128
When a spiral is required to give a traversing motion to a point, it is generally
for the purpose of descrihing a curve on the exterior or convex surface of a
cylinder. In these cases, as we have shewn in the article B 10, the arrangement
is much simplified by dividing the movement, or converting it into a circular and
a rectilinear motion. A rectilincar movement of conversion may be given to the
cylinder on which the spiral is to be described, in the direction of its axis, while
the point or tracing tool moves rouiid it,; or tlie cylinder may have a movement
of rotation on its axis, while the tracing tool traverses in a line parallel to the
axis of the cylinder. The latter method is more generally convenient, and is
therefore adopted in the machinery used for cutting screws of large dimensions:
An engine upon this plan has been erected at Chaillot, and another by Sa-
leneuvc.
The following description will explain the elementary construction of this use-
ful engine. F G in the figure represents the cylinder, by whose action the recti-
linear motion is produced, and communicates it to the tracing tool by means of
its nut P; it has a rotatory motion on its axis, aud is secured in its position by
the collars H and I. E is a toothed wheel set upon the upper extremity of the
guiding cylinder F G, and C is the cylinder on which the required screw is to
be cut; it is mounted upon centres, and a toothed wheel D is fixed on its
upper extremity; the cylinders C and F G must be set perfectly parallel to
each otlier. A is a third or auxiliary wheel which drives the wheels D and E;
the wheel A must be capable of adjustuient, so as to accommodate itself to any
required change of the wheel D, for the purpose of varying the relation between
the radii of the wheels D and E. If the diflference between these should be so
considerable as tliat. the fixed distance of the two cylinders prevents its being
effected by the wheels D and E themselves, and circumstances should also
render it impossible to change the guiding cylinder, the difficulty will be ob-
viated by removing the wheel A, and substituting another wheel with a suitable
pinion.
H 10.
The machine represented in this figure exhibits a method of superseding the
guiding cylinder or screw of the last figure. A rack is here substituted, the ree-
tUinear movement of which is produced by tliat of the cy linder on which them
required screw or spiral is to be cut. The practical resuit will be the same as
under the last arraugement, but the machine will probably not unite ali the ad-
vantages of the former. We give this example however principally to cultivate
the liabit of eonsidering every practicable combination, previous to a final deter-
mination upon any.
The required rectilinear movement may also be communicated to the tracing
tool by means of an inclined plane, as we have shewn in our figure H 1, piate 1.
By an arrangement of this sort, the effect of every possible variety of screw
may be obtained simply by varying the inclination of the guiding plane. This
macliinerv will not be found suitable to the scale of dimensions required for cut-
ting screws of large dimensions; but for screws of ordinary size, it may be
applied witli great facility, and will be found perfectly practicable.
The inclined plane in its applieation to this purpose may receive its move-
ment either by a rack which Works with the pinion D, figure C 10, piate 8, or
by the action of a screw placed at right angles to the cylinder on which the
required screw is to be cut, Ferdinand Berthoud, in his Essai sur 1’horlogerie,
Paris, 1786, vol. i. page 150, describes an engine for cutting fusees, in which
an inclined plane is used to guide the tracing tool, and is moved by a rack and
pinion.
I 10.
The machine here shewn, is a modification of the mechanism described in our
article E 10. We extract the following account of it from the work of M. Prony,
entitled—Nouvelle Architecture Hydraulique, vol. ii. page 141.
The author says, Cf We extract the following description of this instrument
“ from Adams’s work on mathematical instruments entitled—Geometrical and
“ Graphical Essays, &c. London, 1791. The inventor, however, appears to be
<< Jean Baptiste Suardi, who has himself described it in an Italian work, entitled
" Nuovo Istromento per la Descrizione de diverse Curve antiche e moderne, &c. ;
and he gives it the appellation of-—Geometric pen.
“ The Geometric pen is represented in an horizontal plan in the figure; it is
" fixed upon a table or drawing board by means of the arms A, B and C; the
“ heads a a of two of these arms revolve on a common axis, so that they may be
s130
“■ brought into the direction of the third arm at pleasure; and also for the pur-
" pose of rendering the instrument more portable.
At the lower part of the axis D, which is fixed, and is of one piece with the
‘f supporting arm C, is fixed a toothed wheel i, which may be changed occasional-
“ ly, but when in use,, is firmly attached to the axis D and is also immoveable.
tf E G is a bar or arm of metal, open, or double horizontally in the greater part
" of its length, its extremity E is held between the piece k, and the wheel i,
“ but having free liberty of motion about the axis D. A sliding nut b is ar-
“ ranged to slide at pleasure along the opening or groove of the arm E G, and
“ can be tightened and fixed at any required point of its length. This nut carries
‘f a second toothed wheel h, which may be changed when required, and accord-
" ing to the situation of the nut b on the arm, may either act immediately on
" the wheel i, or may receive the movemeqHj>y an intermediate wheel as is
" shewn in the figure.
“ The axis of the toothed wheel h is fixed in a cylindrical stud which is attached
“ to a lower clip piece c; a bar f g slides in this clip, and carries a pencil K
" at its extremity, by which the required curve is to be described. The pencil
“ is adjustible at pleasure as to its distance from the axis of the wheel h, by
“ means of the clip c, in which the arm f g readily moves.
“ This arrangement of the instrument being clearly understood, it will be
“ evident that if the arm E G be moved about the axis D, the toothed wheel h
“ will perform an entire movement of conversion about that axis, and a particular
" movement of rotation about its own axis; the ratio of the angular velo-
“ cities of these motions, depends on the intermediate toothed wheels, and the
“ relation of the respective numbers oftheir teeth. The clip piece c, and the pen-
" cil K have also a movement of rotation with the wheel h about its centre, besides
“ the general movement about the axis D; and the curve which will be described
“ by the pencil K will be determined by the ratio of the angular velocitiesabove-
“ mentioned as well as by the relation between the radii D b and b k.
‘‘ These relative proportions may be varied at pleasure, either by applying
“ different combinations of wheels, or by a different adjustment of the arms E G
“ and f g in their respective clip pieces; it is therefore evident that the instrument131
“ is capable of producing an infinite variety of lines, ali of which shall differ from
“ circular 1 in es, and which nevertheless will be produced by a combination of
(e circular movements. A moderate acquaintance with geometry, will enable
“ the reader to practice himself in devising combinations for the production of
te given curves.
“ Adams also asserts, that the principle of this machine was applied by Bolton
“ and Watt to their improvements of the steam engine; and this has since been
“ confirmed.”
K 10.
In this fi gure, A represents a sqaare piate; B a cylinder fixed on its sur-
face ; its edge is grooved so as to become a sort of pulley; ab c, d ef, are two
ropes or bands which pass round the cylinder B on opposite sides, the termina-
tions of one of those bands are in the points a and d on the left hand bar of the
figure; those of the other are in the points c and f on the opposite bar of the
figure ; the bars to which these bands are thus attached are placed parallel to
each other, the points of attachment are certain pins which are set on each bar
for that purpose. Now if an alternate rectilinear movement be given to the
last mentioned bar, in the direction of its length, the piate A will also assume
a similar and corresponding movement, but will at the same time have a rotation
on the centre of the cylinder B, every point of the surface of which, except
that which marks its centre, will decribe an epicycloidal curve.
We have seen this contrivance applied to machines for grinding and polishing
mirrors.
L 10.
In this figure we have a front, and a side elevation of the subject,with the
same corresponding letters of reference.
A B represents a fixed bar, fitted with a line of projecting pins a a, &c. ;
EDE is a crank movement; C D, a vertical bar whose lower extremity C oc-
cupies the space between two of the pins a a of the cross bar AB, while its
upper extremity D, which terminates in a ring is attached to the end of the
crank arm EDE, so that on the rotation of that axis, the bar CD has a move-
ment compounded of an alternate rectilinear motion, and an alternate circular
s 2132
inotion; by this compound motion, every part of the bar C D will describe a
curve which assumes the fisure of a heart, of different dearrees of elono-ation the
point or most acute portion of which is always in the direction of the fixed bar A B.
N is a square piate carrying a ratchet wheel M: this piate may be fixed in any
part of the bar C D, and should have a free motion of rotation upon an axis passivi g
through the centre of the ratchet wheel M. E F G H is a claw piece ter-
minating at E in a ring through which the end of the crank axle passes,
and previously passing through a ring F which is moveable on its own axis,
and is attached to the vertical bar C D, the rotation of the ring P on its axis
allows the claw piece to oscillate about E, so that, at each revolution of that
axis, the claw piece makes a double oscillation, and its curved termination G H
is so formed that, when the extremity D of the vertical bar is at its greatest
distance from the pins a a of the horizontal bar A B, the extremity H of the
curve G II will have caused a small circular motion of the wheel M on its centre ;
by its action on the ratchet teeth, and the same effeet will be repeated at each
successive revolution of the axis E.
This meclianism has been adopted for the purpose of polishing mirrors, a
description of the machine is given in Bailey’s work, vol. ii, page 142 ; a model
of it may also be seen in the Museum of the Repository of Arts and Trades in
Uo 1*1 CL
M 10. Piate 11.
In our article H 10 we have explained that an inclined plane may be applied
to give the required motion to the tracing tool in the manufacture of screws of
ordinary dimensions; and that the inclined plane might receive its movement
either by a rack, or a screw placed at right angles to the cylinder under opera-
tion ; we referred to Berthoud’s description of an engine for cutting fusees to
shew the application of the first mentioned of these two methods. We shall now
give an example of the second method for screws of small dimensions, such for
instance as those usually termed wood screws used in the general operations
of carpentry, &c.
A A' is the cylinder on which the ‘required screw is to be cut; it is supported
by the two uprightpieces or puppets F and G, at the extremity A is set a bevelled133
toothed wheel C, the moving power used to give the cylinder the necessary ro-
tation, is applied at the extremity A'; the axis B B' is perpendicular to the cy-
linder AA'; and is supported by the two upright pieces or puppets H and I, and
carries a bevelled toothed wheel D working with the wheel C ; the portion gh
of the axis B B' has a screw already formed on its surface. E is a bar of metal
on which a sliding piece traverses, carryingthe cutting tool M; tliisbaris either
of triangular, or quadrangular forni, and is supported by the two puppets F and G.
abcd is a large and deep mortice formed in the plane on which the supporting
pieces or puppets F, G, IT and I are placed and supported. e f b d is a bar whose
thickness is equal to the depth of the mortice a b c d ; it moves within the mortice,
and has a free sliding motion throngh its entire length. The two upright pieces
or puppets K and L are placed upon the bar e f b d ; the first of these terminates
in a cylinder which has a circular aperture through which the axe B B' passes,
and the second of them L, terminates in the nut of the screw gh. At
the extremity ef of the bar efbd is fixed the bar esi; the bar ik has a
motion of rotation about the point i as a centre; it has a longitudinal opening
or groove 1 m, into which passes a small cylinder attached to the sliding piece
M. p and q are balls which form the upper terminations of two small cylinders,
which project one of them from the bar efbd, the other from the bar ik;
and they have each free motion of rotation on their axes. The portion n o of
the arm or rod n r, is cylindrical and passes through the circular aperture of
the ball p; it is at liberty to turn freely, but has no sliding motion ; the other
portion o r, of the same rod n r, has a screw already cut on it, and it passes
into its nut which is cut within the ball q.
This description being understood, it will appear tliat if the cylinder A A'
be made to revolve, the circular motion so produced will be transmitted to
the axis B B', the bar efbd will be accordingly set in motion, and will carry
with it the arm or bar i k. The angle of inclination of this latter may be
varied at pleasure by means of the adjustment afforded by the rod n r; it will
thus perform the office of an inclined plane, and will effect the guidance of the
cutting tool M with the velocity which may be required.m
N 10.
The arrangement L 1 miglit also be used in the manufacture of screws of
small dimensions, thus: let M G in the fi gure represent a portion of an axis or
spindle, comprized betwcen the two supporting pieees or puppets r and p, and
on which it is required to c.ut a screw, and let the portion A G of its prolongation
be supposed to have a screw already cut upon it; this portion is supportcd by
the puppet q; the screw A G passes into the nut s, and is not at liberty to tum.
The bar A B is carried by the nut s, and has a free rotation on the point A; a
longitudinal groove or opening n m admits the fixed cylindrical stud c.
The bar CD slides between the apertures of the three puppets r, p and q;
it carries the cutting tool K, and the perpendicular arm E F. From a part of
this arm, there projects the cylindrical stud a, which passes through the groove
nm of the arm AB. If the axis AM be made to revolve, the nut s will advance
towards G, and will carry witlx it the bar C D; the cutting tool K will conse-
quently move with a velocity which may be varied at pleasure.
An application of this arrangement to a machine for cutting fusees is shewn in
Thioufs Traite d’horlogerie, vol. i, page 70.
SECTION XI.
To convert direct circular motion, of uniform velocity, or which is variable ac-
cording to a given law, into alternate motion in a given curve, of velocity
similar to that of the original motion, either equahle, or variable according
to a given law, and in the same or in different planes of direction.
We are not acquainted with any direct method of solution of this problem;
but if the given direct circular motion, be converted into alternate circular
motion, by means of any of the methods exhibited in the examples of Section 9,
tbese may be again converted into alternate motion in a given curve, by any of
the methods shewn in Section 10, and by the arrangement A 20.135
SECTION XII.
To convert direct motion in a given curve, and of velocity either equable or vari-
able by a given law, into alternate rectilinear motion ; of velocity similar to
that of the original motion, either equable, or variable according to a given law,
and in the same, or in different planes of direction.
THE given movement must be converted into a direct circular movement by
some of the methods given in Section 10; and the direct circular movement
thus obtained, changed into an alternate rectilinear movement, by Section VII.
SECTION XIII.
To convert direct motion in a given curve, and of velocity either equable, or vari-
able by a given lazc, into alternate circular motion ; of velocity similar to that
of the original motion, either equable, or variable according to a given law,
and in the same, or in different planes of direction.
THE given movement will be converted into a direct circular movement, by
some of the examples of Section X.; and the movement so obtained, changed
into an alternate circular movement by reference to Section IX.
SECTION XIV.
To convert direct motion in a given curve, and of velocity either equable, or vari-
able by a given law, into motion in a given curve ; of velocity similar to that
of the original motion, either equable, or variable according to a given law,
and in the same, or in different planes of direction.
A 14.
IF the given movement be converted into a direct circular movement by the
methods shewn in Section X, the required movement in a curve, may be ob-
tained from the direct circular movement so obtained by the same Section.136
B 14. Piate 8.
The subjeet of this article is a pantograph, as improved by Langlois, a mathe-
matical instrument maker. A detailed account of this instrument may be seen
in the Machines approuvees par l'Academie des Sciences, Vol. vii, No. 460. It
is used for the purpose of tracing’ similar figures of any description in any relative
proportions whicli may be required, and with any given velocities.
In the Annales des Arts et Manufactures, vol. v, page 59,, we find the descrip-
tion of a machine for copying drawings and writings, which the inventor terms
an Autograph. It is a modification of the Pantograph.
SECTION XV.
To convert direct motion in a given curve, and of velocity either equable, or vari-
able by a given law, into alternate motion in a given curve, of velocity similar
to that of the o?'iginal motion, either equable, or variable according to a given
lato, and in the same, or in different planes of direction.
THE given direct motion in a curve may be converted into alternate circular
motion by the methods shewn in Section VIII.; and the alternate circular
motion so obtained, into an alternate motion in a given curve, by the methods
shewn in Section X.
SECTION XVI.
To convert alternate rectilinear motion, of velocity either equable, or variable
by a given law, into alternate rectilinear motion, of velocity similar to that
of the original motion, either equable, or variable according to a given law,
and in the same, or in different planes of direction.
THE given alternate rectilinear motion, may be converted into circular
motion by the methods given in Section VII.; and the motion so obtained,
into alternate rectilinear motion, by the subjects of the same Section.
Ali the movements described in Section I. will also furnish a solution of this
problem.137
In the " Machines approuvees par 1’Academie,” Vol. v, No. 350, we find a
macliine described by M. Du Buisson, in which an inclined plane is applied to
produce the required alternate rectilinear motion. The description of the
machine is introduced to contribute to an history of machinery.
The small pumps which are used on board ships, and frequently for drawing
liquore, in which the action is produced by an alternate motion of the operator’»
hand, is composed of a cylindrical tube or pipe, having a valve at its lowrer extre-
mity, which is immersed in the liquid. It is sometimes indeed constructed
without any valve: in this case the effect of the machine is produced by a dex-
trous application of the operator’s thumb, at the upper extremity of the tube.
These engines also belon«' to this division of our work.
o	O
SECTION XVII.
To convert alternate rectilinear motion, of velocity either equable, or variable by
a given law, inio alternate circular motion, of velocity similar to that of the
original motion, either equable, or variable according to a given law, and in the
same, or in different planes of direction.
A 17.
Several of the movements described in the Section III. and VII. will also be
classed in this Section.
B 17. Piate 9.
In this subject, A B in the fi gure represents a lever, moving on the axis C as
a fulcrum, w hich is the centre of the semicircle D E F fixed to A B. The extre-
mities of a chain D G H K F are attaclied to the points D and F of the bar A B ;
it is adjusted by two pins so as to allow of being lengthened or shortened as oc-
casion may require. The chain passes over two fixed pullies G and K. Under
this arrangement the alternate circular movement of the lever A B will produce
the alternate rectilinear motion of the portion H of the chain, a reciprocal move-
ment will also be affbrded by this machine.
This movement has been successfully applied to a machine for cutting the tops
T138
of piles situated below the surface of the water, and is in practice one of the most
simple and effective contrivances for that purpose.
C 17.
This combination of levers in zig-zag arrangement, is well known ; it is applied
in the contrivance of various toys for children. It has been also applied to the
construction of a machine for raising sunken vessels, by Du Vivier. See Ma-
chines approuvees par 1’Academie des Sciences, Vol. vi. No. 429. We also find
several applicatioris of the same movement to the construction of various machines
in De Besson’s work, Theatre des Instruments de Mathematiques, already spoken
of; but these are all of them more or less imperfect. This author proposes to
communicate the alternate circular movement by a fixed adjusting screw, this is
composed of two distinet screws having their respective threads in opposite direc-
tioris. The screw by its rotation produces the alternate approach and separation
of two nuts fixed at the extremities of the two lower or first levers of the zig-zag
arrangement. This piece of mechanism is also applicable to many other prac-
tical purposes *.
The pincers generally used for lifting or drawing up heavy bodies from the
bottom of the sea, is also an application of the same principle.
The coramon spinning reel is an highly ingenious and useful application of
this combination of levers.
In the Annales des Arts et Manufactures, Nos. 19 and 20, we find the descrip-
tion of a pump on a new construction, presented to the Minister of the Marine,
by M. Berger.
This is a double piston pump, which seems to embrace advantages deserving
attention. A report was made to the Institute on the subject of this pump by
Messrs. Borg, Monge, and Leveque; it is inserted at length in the abovemen-
tioned numbers of the Annales des Arts et Manufactures, and merits an attentive
perusal. It is here asserted that the idea of this engine did not originate with
* Several applications of this machinery may be fouod in the first volume of Leupold’s u Theatrum
Machinarum Generale.’» Leipsic3 1724.139
M. Berger, (and to this M. Berger appears to assent) but that the inerit of the
invention belongs to Mr. Noble, an Englishman, whose pump on this construc-
tion was readily admitted into the British naval Service, and was there substituted
for the usual chain pumps. It appears that these pumps were first introduced to
actual use in the Windsor Castle, a British seventy-four gun ship, in theyear 1790,
and that their use has been since continued with mucli benefit to the Service.
M. Berger proposes two methods for working this pump, one of which however,
the reporters reject as impracticable: but they consider the other to be preferable
to the crank rnovement adopted in the English Service. The following description
of the method they approve is extracted from their report:
“ The principal part of the arrangement is a lozenge figured combination of
“ four iron bars orrods ab, bc, cd, da, connected at their extremities by hinges
“ or pin-joints, so that they have free motion on them, and the component pieces
“ or bars can either extend or close their angles, and arrange themselves in
“ lozenges of different figure. This combination is represented in the figure as
placed in a vertical position, so that one of the diagonals of the lozenge it coni-
poses is in an horizontal position, and supported by two bars or pillars a e, c f
of equal height, in such a mannerthat the pin which attaches the contiguous sides
of the figure shall also attach those sides to the corresponding supporting pillar.
It is evident, that in this position, the other diagonal of the lozenge will be in a
vertical position; this must correspond with the centre of the pump barrel and
be situated accurately in the prolongation of its axis. To the upper extremity of
this diagonal are attached the two rods of the lovver piston, and to the other ex-
tremity are fixed those of the higher or upper piston; and the same pin which
attaches the contiguous bars to that diagonal also attaches them to the piston
rods.
It will be understood that, in order to alter the angles which the bars of the
figure form with each other, and so extend or reduce the dimensions of the dia-
gonals, the two supporting pillars a e, c f must have liberty of motion. They are
therefore set on a cross piece on the joints e, f to which they are attached by a
pin, and have thus a rnovement of rotation in the same plane as that in whieh
the bars of the arrangernent are situated.
t 2140
The construction and disposition of this mechanism being understood, it will
appear tliat by causing the horizontal angi es of the figure to approach each other,
the upper angle is made to rise, while the lower angle is by the same action,
made to descend in the same quantity ; and if on the contrary, the horizontal
angles of the figure are made to recede from each other or encrease their distance,
the upper angle will descend while the lower angle will rise ; thus the action of
the pistons is produced. It will be seen, tliat in this arrangement the maximum
range of each piston is equal to the side of the figure ; the action of the pump
does not however require the maximum range of the pistons, nor indeed would
it be possible to obtain it in practice; it being necessary for that end that the
supporting pillars should vary very little from a vertical position. M. Berger
considers the best dimensions for the figure to be about 22. 2 inches in each side,
and that 18 inches will allow sufficient range for each of the pistons.
In this action of the pistons it will be understood, that given points in the sides
of the figure are elevated and depressed proportionally, so that the range of each
piston, and the vertical path of any given point in one of the sides of the figure,
are constantly in the ratio of the distance of the point of suspension of the piston,
and the point from which it acts, from that centre of motion of the lozenge
which is situated at the extremity of the eontiguous supporting pillar. The ho-
rizontal line which joins the middle of the lower ends, will therefore be elevated
or depressed a quantity equal to one-half the range of each piston. M. Berger
transmits the action of the moving power directly to an arm placed on this line
by the following arrangement:—Each lower piece of the figure is perforated in
its middle by an iron axle, to these are fixed two naves of wood of about 3. 75
inches in length, the projecting portion of each axis is cylindrical, and receives a
small metal roller having a flanch or projecting shoulder on its outer end ; these
rollers support a frame which eacloses the lozenge, which passes into longitudinal
openings made in the side pieces of the frame, and the whole is firmly held to-
gether by nuts, as in the modes of fastening practiced in coach building. The
length of the openings in the sides of the frame are determined by the raugo
which may be required for the pistons. To the middle of each of these sides is
fixed an axis: it is necessary that these should be accurately centred, or placed141
accurately opposite to each other, having to perform the office of a single axis
passi ng through the entire width of the frame; these axes pass through the sides
of the frame of a set of lever handles which encompass the whole machine, nearly
resemblivig the arrangement of working handles by which the common fire-engine
is put in action. The axis of motion of the set of lever handles is supported by
two upright pillars C D, the arrn which works the lozenge is divided at one-third
of its length by the arm of the enclosing frame.
It will be evident that under this arrangement, if the power of men be applied
to the bars it will operate to raise or depress the frame, because the flanched
rollers passing through the openings in its sides will allow the alternate opening
and closing of the lozenge frame, and thus effect the required action of the
pistons. It will also be seen that the extent of the motion of the frame will be
but one-half that of the pistons, and that the men whose action is directed on
the bars, will have to perform a motion through the same space only, as that
traversed by the pistons, which will act in a perfectly equal and simultaneous
manner, and in the reverse direction. Lastly, the piston rods will preserve the
same vertical positions, because those points of the lozenge frame to which they
are attached, describe in equal times, two equal and similar curves in vertical
planes: these are placed back to back, having their concave sides in opposite
direction; those points therefore can only follow the direction of their common
tangent, which is vertical.
The statement respecting the range of the pistons being double that of the
frame by which they are worked, should not be understood as strictly correct,
for in the organization of the engine which we have described, it will become
rather greater, from the effect of the rotation of the supporting bars a e, c f,
because, by that rotation the horizontal diagonal constantly preserves its hori-
zontal position, during its elevations and depressions; this circumstance is how-
ever rather advantageous to the general effect of the engine than otherwise.
In the figure D 17, we have omitted the frame which encloses the lozenge
frame, and we have shewn but a small portion of the lever handle g i; upon one
side of the portion shewn in the piate, a curved groove n m k is cut, into which
the axis n passes, which is fixed to one of the lower sides of the lozenge; and142
this axis has a small frietion roller upon it, for the purpose of facilitating the
motion. This arrangement appears to us to be more simple than that proposed
by M. Berger. Notwithstanding the omission of the parts of the original figure
above-mentioned, and the other alterations, an attentive reader will find our de-
scription perfectly intelligible. Carcful reference to the articlcs A 7, B 7, and
K 7 of this work will point out the method of describing the curve rcquired io
this instance at nmk.
E 17.
The alternate circular movement of the beam B produces an alternate reeti-
linear movement for the rods M N and P Q, by means of two portions of chain
which are attached to each of the circular curved picces at the extremities of the
beam, and set in contrary directions. The steady motion of the rods M N and
P Q is provided for by making them slide through the picces p, q, r, s.
In Berthelofs work entitled, La Mechanique appliqee aux Arts, vol. i, page 13,
we find the description of a mill constructed on this principle. An alternate cir-
cular lever motion is couverted into an alternate rectilinear motion, by means of
two chains wliich act on two rods, one of which is raised while the other is de-
pressed ; each rod carries a click piece which acts on the same side of a ratchet
wheel, and so communicates to it a direct circular motion. Upon the axis of the
ratchet wheel is fixed the large wheel which drives the lantern pinion of the mill
shaft.
In volume i, page 36 of the same work, he applies the same mechanism to a
pulverising engine: in this instance the shaft of the ratchet wheel carries fixed
projecting pieces which act to raise the pestles or beaters; and in the same volume,
we find the same principle applied to raisjng the hammers of large forges.
Other examples of the application of this contrivance may be seen in the
Annales des Arts et des Manufactures, vol. xii, page 83, in a memoir entitled—
Description de plusieurs Nouvelles Pompes a Feu, &c. Some interesting obser-
vations occur in this memoir respecting the high state of improvement of our
steam engines, as relates to the extensive variety of their dimensions and powers j
and the consequent facility with which this important auxiliary can be adopted
in operations of any given scale, The recent improvements of Woolf, as respecta143
the economy of fuel may also be seen in the Annales des Arts et des Manufac-
tures, vol. xx, page 294; and in the Bibliotheque Britannique, vol. xxviii,
Nos. 221 -222.
F 17.
This is an engine or tool familiarly known in the practical arts, under the ap-
pellation of Driil, Trepan, or Borer.—A is the spindle or stem ; BB the cord or
band; CC the cross piece; D thefly; E the Socket ; F the driil, of which G
is the cutting point.
The alternate rectilinear movement of the cross piece C C produces the alter-
nate circular movement of the driil. This method of boring has the peculiar dis-
advantage of wearing the cutting tool very quickly ; and which those boring
engines are not subject to which have a direct rotative action, or always in the
same direction.
G 17.
AB is a rod or bar, sliding within the pieces n m ; the lever D F, turning on
its fulcrum or axis E, communicates by means of the arm CD, its alternate cir-
cular motion to the bar A B, w'hieh has its alternate motion in a right line; a
feciprocal action wilt also take place in this machine. . This movement is appli-
cable to ptimp work. Among the pumps made on this construction, and which
inerit partitular attention, may be mentioned Franklin’s double piston pump, a
description of which will be found in the Bulletin de la Societe d’Encouragement,
ofthe 15th year—August 1816.
H 17.
This figure shews the mechanism used in the double injection steam engine,
for the conversion of the alternate rectilinear motion of the inflexible rod ofthe
piston, into the alternate circular motion of the beam, (and reciprocally). The
foilowing description of it is given by M. Prony, in the second part of his
Nouvelle Architecture Hydraulique, page 56.” '
“ The parallelogram a b c d attached to the beam by the points' a and c
" which, with respect to the beam, are fixed points ; but the sides of the figure
‘c are at liberty to alter their inclination with respect to each other, by means of
“ their extremities being jointed together, that is to say, constructed with clips144
“ or collars, which are fitted on tlie horizontal axes. (At page 116 of tlie author’s
“ work, lie gives a detailed description of the construction of this meelianisrn).
“ The axes in the points a and c are in the same plane vvith the centre, or axis
” of rotation O of the beam.
" Further, the angle d of the parallelogram is constantly retained at a de-
“ termined distance from the fixed point f', by means of the metal rod f' d,
the extremity of which has also a clip or collar which fits upon the centre or
axis passing through the point d.
“ This being clearly understood, if we imagine the angle b to be urged or
“ drawm in a vertical direction, the effort will force the sides baandbd to
‘e assume an inclined position as in the figure; the points or centres a and c
“ will describe circular ares, of which the point O will be the centre, and the
fC point d will describe a circular arc having f' d for its radius. But the curves
“ described by the points a, c, d, being thus fixed and determined, the curve
" described by the point b will also be fixed and determined; and it will be
(< easily seen by inspection of the figure, that when the motion of the beam acts
“ to drive the point b out of a vertical line in one direction, the eflfect of the
“ rotation of d about f', .will be to drive it also out of the vertical line, but in
the opposite direction , and therefore that these counteractions may be so com-
“ bined and arranged that the cui’ve described by the point b will deviate so
little from a vertical right liue, that in practice the difference may safely bo
« disregarded.”
The theory of this parallel motion is also detailed in a lucid and satisfactory
manuer in the same work, from page 137.
I 17.
A different solution of the same problem has been given by M. de Bettancourt,
M. Prony gives the following account of the method, at page 67 of the same
\vork,
Two beams of wood ab, d O haverotatory motion about the points or centre^
a and O ; their extremities b and d are connected by the iron rod bc' d, having
joiats at b and d. The lengths ab and d O from centre to pentre of the joints*145
are equal: the sum of those lengths a b -f d O is equal to the distance of the
point a from O on an horizontal projection, or measured horizontally, so that,
when ab and dO are parallel to each other, or each horizontally situated, a right
line passing through d and b vvill be a vertical line ; and since the length of the
piece b d from centre to centre of the pins, is equal to the vertical distance of the
points a and O, bd takes a vertical position vvhenever ab and dO become ho-
rizontally situated.
By means of tliis arrangement, if the points b and d do not describe very con-
siderable ares above and below their horizontal positions, on the levels respec-
tively of the points a and O, the middle point c of the bar b d will have a scnsible
motion in a vertical right line. In practice it will be found that the elevation or
depression of the point b, with respect to the point a, will be more nearly equal
to the elevation or depression of d with respect to O, as the motion of the points
b and d departslessfrom their horizontal position ; vvhence it followsthat the ares
described by the points b and d, may in such case be considered as equal. Tliis
hypothesis being admitted, the points b and d will be always at. an equal dis-
tance from a vertical line from which the points a and O are also equi-distant t
therefore if c1 be placed in the middle of b d, it will be constantly situated in
the above-mentioned vertical line. This vertical line coinciding with the common
axis of the steam cylinder and its piston rod c! c, it will only be necessary to at-
tach an horizontal axis to the upper end c' of the piston rod, which shall turn in
a collar formed in the middle point of the bar bd, and the conditions of the
problem will be satisfied. A theoretical demonstration may be seen at page 123
of the same work.
K 17.
This figure represents the common Drill-bow—an instrument too familiarly
known we presume, to need any particular description.
We shall merely remark that if the alternate rectilinear movement of the drill-
bow communicates an alternate circular movement to the spindle, about which
the bow-line is wound, it will not be difficult to give it a direct. and continuous
circular motion ; for this purpose it will only be necessary to place a fiy-wheel on
the spindle, and by a dexterous management of the bow, to make it act on the
v146
eylinder of the spindle in onedirection only, and which may be accomplished by
a little attentive practice. This contrivance has been applied by M. Raux to
give motion to a thread machine, of his invention, and which received the appro-
bation of the Institute, in the year 1806.
L 17.
In this movement, if the wheel A be made to revolve in one direction, the
wheel B will revolve in the opposite directiori, and they will each act on the cor-
responding racks of the frame which encompasses them, so as to communicate
a rectilinear movement to the bar C D; this movement might consequently also
be placed in the seventh range of movements in the table.
M 17.
This arrangement is a modification of thelast, and is capable of several highly
useful applications.
If two toothed wheels be placed upon an axis, and two racks placed diametri-
cally opposite to each other are made to work with each of them, the alternate
circular movement of the axis will communicate an alternate rectilinear movement
to the racks, and the extremities of the racks will advance to the axis or recede
from it, in a uniform manner. Spinning reels have been constructed on this
principle; cylinders of variable diameter might also be thus constructed (see our
article C 7.) by properly arranging a sufficient number of wheels and racks.
N 17.
The conversion of an alternate rectilinear motion, into alternate circular.
From the Annales des Arts, No. 43.
In the figure, abcd represents a bar or rod, having its direction of motion
confined to a groove; a second bar t v d k v' t is attached to the first by the joint r,
so that the two bars are at liberty to open and shut upon the centre r, sirni-
larly to the common folding pocket rule. A piate of metal 1 n h m, which moves
parallel to the line b d, carries the two pins p and q, which are lodged in the
hollows, vt' and vt' cut in the bar tvdkv't.147
It will be seen that by this arrangement, if the piece lnhm moves towards the
end e of the machine the two jointed bars being supposed to be opened on the
joint r, they will be shut by the action of the pin q upon the curve V v', and
afterwards carried forwardsby the continuation of the motion ofthe piece lnhm;
and the reverse of this operation will take place, when the movement of this piece
is made in the opposite direction. This mechanism has been applied by M. Droz,
in the coining press, to the purpose of introducing and shifting tlie pieces.
The alternate rectilinear movement of this mecbanical hand, as it may be
termed, is very slow at the extremities of its course, and accelerated towards the
middle of it, in order to receive the pieces as they fall from the hopper or feeder
of the engine, and to place them under the press without shake, and with perfect
steadiness. This movement is communicated to it by means of a pin *, fixed to
the moving piate lnhm, which passes into an oblong aperture formed at the
lower extremity of the bar £y J; the axis or pin y stands in an horizontal position,
and perpendicular to a plane passing through tlie axis of the screw of the press ;
so that when this lever is moved either in one direction or the other, the pin * is
pushed either back or forwards, and consequently the piate lnhm also. The
upper extremity of the lever 5yS moves between two metal curves which are
described according to given rules, (see our article A 7). Each of these curves
is attached by its extremity to the large screw of the press, and are so arranged
that the pin \ recedes when the screw is lowered, and reciprocally. From this
description the connexion between this piece of mechanism and the press, and
the mode of its action, will be understood. The alternate circular movement of
the engine being supposed uniform, it will be converted into an alternate circular
movement, which shall be slow at the extremities of the oscillation, and acceler-
ated towards the middle ofits course, by means of two horizontal curves forming
a groove, in which the upper extremity of the vertical lever $ y j will move. The
same will take place with respect to the lower end of the lever; in this case, the
same extent of oscillation will be preserved if the axis y is plaeed in the middle
of the lever Jy J; and will become larger or smaller, as it is shifted nearer to,
or farther from the upper end of the lever. This latter irregular alternate cir-
v 2148
cular motion will be converted into alternate circular of tlie description required
by the nature and intention of the engine.
O 17. Piate 10.
In this figure, A B B represents a side elevation of the beam of a steam engine;
G its centre of rotation ; n m an iron rod which is at liberty to turn freely about
an axis b placed at the extreinity A of the beam, and which divides the rod
n m into two equal portions; the rod n m is attached by the extremity n to the
piston rod f, and at the other extremity m, to the rod p q, which turns on the
fixed axis q.
Under this arrangement, we will suppose to be given—Ist. The dimensions
of the beam of the engine A B B.—2nd. The position of its centre of rotation G.
—3rd. The arc bea which the extremity A of the beam will traverse at each
oscillation, and which will be tangential to the direction of the piston f.—4th.
The length of the rod n m.
From these data it is required to determine the length of the rod p q, and
the position of its centre of rotation q, so as to ensure, as nearly as possible,
the rectilinear direction of the piston.
The positions of the three points m, m', m", will be determined, so as to indicate
the respecti ve situation of the extremity m of the given rod n m, at the com-
mencement—towards the middle—and the close of the oscillation of the beam ;
and so that in those three positions, the other extremity n shall be situated ac-
curately in the direction of the piston rod f. If a circle be described which
shall pass through these three points ; its radius will be equal to the required
length of the bar p q, and its centre so determined will represent the required
centre of rotation q.
The curve described by the extremity n of the piston rod f, will pass through
the three points n, n7, n", and will approximate to tt right line, as the arc a c b
described by the extremity of the beam, is smaller.
The same course of proceeding will serve to determine (in the figure H 17,
piate 9.) the length of the rod i1 d, and the position of the point of rotation f';149
and in the figure I 17 of the same piate, will also serve to determine the length
of the bearn a b, and the position of the centre of rotation a.
P 17. Piate II.
In our article G 8, we have given a description of a piece of mechanism in
general use in our cotton spinning uiachinery. In the operations of vvool spin-
ning, the motion of the carriage is not uniform through its entire course:—it
commences by traversing a space fk with an uniform motion, the distance,
this generally extends is from twelve to eighteen inclies, according to the quality
of the wool; during this interval, the machine thickens a certain quantity of the
material, which must. be lengthened out to about four feet; the twisting should
be encreased in proportio» as the thread lengthens, and the motion of the fusees
being uniform, the rate of motion of the carriage must be gradually slackened as
the thread lengthens. The effective performance of this operation is the resuit
of long practice alone ; and our woollen mauufactories are yet unprovided with
any regular method for the purpose, depending solely on the mechanical dcx-
terity of the operatore, vvho regulate the motion of the carriage with the left-hand,
while with the right they produce the uniform rotation of the wheel which gives
motion to the fusees. The address required for the due performance of this dit-
ticult operation is, as may be conceived, to be acquired only by a course of toil-
some and attentive practice which generally occupies a long term of servitude.
These serious disadvantages arising from the rnisapplication of labour vvouhl
be completely obviated, as well as a satisfactory general improvement effected,
by the general solution of the following problem.
In the mechanism represenled at G 8, piale 5, let the rotalory movement oflhe
pulley B be uniform, and let it be required to determine the means of rendering the
velocity of its movement of conversion, variable at pleas ure.
The following course of proceeding will afford the required solution : A drum A
(figure P 17, piate 11.) is substituted for the pulley B of the figure G 8, piate 5 ;
the figure of the drum wheel will be determined by the nature of the velocity of
the required conversion. From the extreinity a of the drum there projects a neck150
having a spiral cut upon it which after a certain number of eonvolutions, terminates
at its other extremity b. Let f h represent the entire course which the carriage
will perform, and let h g be taken equal to the height a c of the drum wheel A,
let a rope or band be attached to the point f, and a second to the point g ; each
of these must be equal in length to the distance f g ; the other extremity of the
first band is attached to the point a, and the second to the point b, after being
coiled on the spiral in opposite directions. The two cords sliould be in contact
always at the same point of the the drum A.
It will be seen by this arrangement—1. That if the drum A revolves uniformly
on its axis, its movement of conversion will vary as the radii of the spiral.—2.
That as one of the bands is coiled by the motion of the spiral, the other is un-
coiled ; and by this means their tension is constantly preserved.—3. That lastly,
the drum A will have no tendency to motion in the direction of its axis a c
This piece of mechanism was communicated to us by M. Sureda, whom we
bave already had occasion to mention in our article O 7.
According to a series of observations made by M. Sureda, in the most careful
manner for the purpose of determining the ratio of the velocities of the carriage,
under the management of the most experienced operators, it appears that at the
end of the first part of its course, the carriage had stili to traverse a distance of
four feet four lines, or 580 lines *; and which was traversed by it, while the
wheel which communicates the uniform motion to the fusee performed ten revo-
la tions : the spaces respectively run through during each revolut ion were as
follows:
* It may be necessary, for the Information of the general English reader, to note that the Freneh
mensure of length termed a line, is to the inch as twelve to one;—58Q lines are therefcre^fonr feet and
four lines.151
Lines.
Duringthe Ist revolution of tlie wheel 112
2nd.......................... 88
3rd.........................  74
4th.......................... 62
5th.......................... 53
6th.......................... 46
7th.......................... 41
8th.......................... 38
9th.......................... 36
lOth......................... 30
Total 580
The first part of its course of one foot and a half, was uniformly traversed in
the time occupied during two revolutions of the wheel.
It vvill readily be conceived that notwithstanding the utmost care and intelli-
gence on the part of the observer, these results may be subject to error; and
we do not consider we exceed the probable extent of such errors in statin°- the
following table of results in correction.
Lines.
During the lst revolution of the wheel 106
2nd......................... 90
3rd........................  76
4th.......................   64
5th......................... 54
6th ........................ 46
7th........................  40
8th.......................   36
9th .....................    34
lOth.......................... 34
Total 580152
In the figure N, piate XI, let the line ca be divided into nine equal
parfs, and through the points of division draw the perpendicular lines
IX VIII VII VI V IV III II I o
M ;y 'y<y >y.y - y.y.y. which shall be relatively as the ta-
bular numbers of the last stated series, and let a curve bhnm be described
through the extremities of tliese lines. Let y represent the ordinates of this
ciirve, x its abeissae from the vertex h, p the distance cd—dd', &c. which is
IX	VIII VII
the measure of separation of the perpendicular lines, y , y , y, &c.—and a
the distance h r from the vertex of the curve to the line ac.
2	3
The well known equation y=p (x—a) in which p=c d—d d', &c. and a—y’
—1=34—1=33. 75 will agree with the observations, as may be shewn by sub-
stituting for x, its values y'—a, y"—a, &c.; in which case we obtain succes-
sively y=f; y=A p, &c. &c.
In practice it may be arranged that the spiral shall make twelve revolutions,
the two first for the first part of the course of the carri age, and the remaining
ten revolutions for the second part of the course; the whole course of the spiral
must be equal to the distance f g.
If the line a c of the figure N be supposed equal to the heiglit of the drum A,
and that $ represents the ratio of the diameter to the circumference, each term
of the last stated series must be multiplied by 1 and the curve bhnm be drawn;
and this will be the generating curve for the surface of the drum.
The drum A will thus be composed of two portions, one aru of a parabo-
loidic figure, by which the progress of the carriage will be duly regulated, during
the second period of its course; and the other, brut, of a cylindrical figure,
which will propel it during the first period of its course, with an uniform velocity.
The drum A may be placed in communication with the mover, or be detached
from it, at pleasure, by the methods already explained; and thus by a suitable
npplication of such a method, the carriage may be retrograded to the point whence
it commenced its course without the necessity of reversing the action of the
mover.153
SECTION XVIII.
To convert alternate rectilinear motion, of uniform velocity, or which varies by a
given law, inio alternate motion in a given curve, of velocity similar to that of
the original motion, uniform, or variable by a given law, and in the same or
in different planes of direction.
TIIE given alternate rectilinear movement will first be converted into an ai-
ternate circular movement by Section XVII, and the movement so obtained
into an alternate movement in a given curve, by Section X.
SECTION XIX.
To convert alternate circular motion, of uniform velocity, or the velocity of which
varies by a given law, into an alternate circular movement, of velocity similar
to that of the original motion, uniform, or variable by a given law, and in
the same, or in different planes of direction.
A 19.
ALL the arrangements contained in Section VIII, and a part of those con-
tained in Section IX, will afford Solutions of this problem.
B 19. Piate 9.
M. Camus in the Receuil des Machines approuvees par l’Academie, Vol. ii,
Nos. 136 and 137, describes some machines of his invention for the purpose of
giving motion to several sieves by one operation.
The entire arrangement in the figure may be reduced to a large table AB CD ;
above the table is placed a plane board E P, supported by two iron axes n, m,
which tura on iron upright pieces, fixed to the table. Upon the prolongation of
one of the axes n m, or upon an arm s, is fixed the pendulum RS; and the
sieves are arranged on the board E P.
x154
The moving power produces thc oscillation of the pendulum R S, and conse-
quently also communicates an alternate circular movement to the board E F;
at each oscillation the edges of the board strike against the table B C, and very
effectively represents the motion usually communicated by hand.
C 19.
In this machinc the cord abc is attached in a to the spring B, and after
being coiled about the cylinder A, is afterwards attached to the extremity c of
the treadle D. The alternate circular movement of the treadle communicates a
movement of the same description to the cylinder A.
D 19.
In this arrangement, the alternate circular movement of the treadle D, pro-
duces the direct circular movement of the fly wheel M, and also a second alter-
nate circular movement in the cylinder A.
E 19.
The Nippers of the Sawing Machine.
These nippers are composed of two pieces of iron abcd, e f g h, which turn
upon the centre or axis i; the extremities ab and ef of these pieces are cut in
a semi-circular form; the interior edge is serrated, they form together the jaws
or head of the nippers. The other extremities bcd and fgh of the same pieces,
terminate in two circular ares dc and gh ; the first of them being toothed on its
outer or convex edge, the latter on its inner, or concave edge. At the middle
point between the interval which separates the two circular ares dc and gh, an
axis C is placed perpendicularly to the plane of the machine ; this axis carries
two pinions n and m, the first of which, n drives the arc dc, and the second m,
the arc gh.
The alternate circular movement of the axis C, operates to open or close the
jaws of the nippers at pleasure.
F 19. Piate 10.
A long bar or plank A B, is traversed in its middle by an axis fixed at theupper end of the upright piece CD. The alternate circular movement commu-
nicata] to the extremity of A B, by the action of a person seated at that point,
and which tends alternately first to elevate it by the sudden action of the feet
downwards on the ground on which they are then placed, and afterwards to pro-
duce its descent, by the effect of their gravity. These movements are communi-
eated conversely to a person seated at the opposite extremity, whose action
similarly exerted, tends continually to encrease the oscillations of the machine.
SECTION XX.
To convert a given alternate circular movement, of uniform velocity, or which is
variable by a given law, into an alternate movement in a given cume, of velo-
city similar to that of the original movement, uniform, or variable by a given
law, and in the same, or in different planes of direction.
A 20.
ALL the movements described in Section X, will afford Solutions of this
problem.
B 20.
This is a turning engine by which screws of any description may be made,
without centres. It is the invention of M. Grandjean, &f the Royal Academy of
Sciences; and is described in the " Machines approuvees par 1’Academie/’ vol. v.
1729, No. 336.
“ This engine is composed of a firm supporting frame or stand A B, and two
“ upright pieces or puppets P Q; these have instead of centre points, two collars
“ S T, which receive the mandrill P H, whose terminations are conically pointed;
“ F H carries the piece R which is to be cut, and also the pulley G which re-
“ ceives the band GO attached to the treadle O. The puppet Q carries an
" iron arm I, to which is attached in I a square H K, also of metal, one ex-
“ tremity of which presses on the point H of P H, and consequently tends to
" pre6s it from H towards F. The point F is supported upon a piece E, which
“ is moveable upon an axis D, at the extremity D of which, the piece D C is
x 2156
“ set upon a square ; and in a groove formed in this piece there runs a sliding
“ piece N to which the band N O is attached, and thence passes to the treadle O.
“ This understood, it will be evident that when the foot is applied to the
“ treadle, it will produce the rotation of F H, and will also lower the piece D C,
tf that this motion of D C will cause the advance of F H from F towards H in
<c a quantity which will be always reciprocally proportional to the distances DN
“ of the sliding piece N from the centre of motion D; and the piece N being
“ moveable, it may be adjusted or placed in any required situation or distance:
“ hence it will resuit that during a revolution the axes will advance whatever
“ quantity may be required, and consequently if the cutting tool be applied at
” R, any required screw may be produced, as was proposed.
" If a spiral or screw be required, the thread of which shall become gradually
‘c closed or finer, it will be only necessary to take ofF the piece D C and substi-
“ tute for it the piece D N C, figure 2, the periphery N V C of which is a curve
“ in which the radii DN, D V, D C encrease as the thread of the screw to be
,c cut is required to close; thus, each point of the curve, as C, V, N, &c. will
,c successively perform the office of an arm or lever of different length, continu-
“ ally substituted for the arm DN, figure 1, which will produce an unequal
“ retrograde motion of F H towards H, and consequently the thread of the re-
‘f quired screw wilLbe gradated as the radii DC, DV, DN.”
C 20.
M. Clairault is the author of a memoir included in those of the Academy of
Sciences for 1734, in which he proposes the solution of several important
problems.
One of these has for its object the determination of the curve M ON, upon
which if the square M C N be moved always in contact, its vertex C shall be
alwavs in the given curve E C.
The required movement of the square may be given by an alternate circular
movement, which by the solution of the problem will be converted into an alter-
qate movement in the given curve E C.
D 20.
In this piate, the figure on the right represents a front elevation, and the157
figure on the left a side elevation of the subject. The same letters of re-
ference are placed as usual to the corresponding parts of the machine in both
figures.
These figures represent the machine used for rifling gun barrels, in the
Royal Arsenal at Versailles.
A A are two upright timbers placed perpendicularly upon the lower or
ground framing B, and the cap piece C C attaches the upper ends of the up-
right timbers; tlie whole composes a frame work, the firmness of which is
farther secured by the auxiliary pieces D and E.
G is a cylindrical roller on the axis of which is placed the toothed wheel H,
and this is driven by the pinion I; the moving power is applied to a winch set
on the axis of the pinion.
a b c d is a carriage which slides vertically in the frame AABCC; two ropes
e e are fixed to the upper cross framing of the carriage, they pass over two fixed
pullies attached to the cap C, and are afterwards coiled on the roller G; another
cord f is attached to the middle of the lower cross framing of the carriage, passes
over a fixed puliey to the lower piece B of the principal frame, and then returns;
and is coiled also upon the roller G, but in a contrary direction to that of the
cords e e.
The carriage carries an iron cylinder gh; theextremity g of which rests upon
ablock of metal, fixed in the middle of the upper surface of the lower cross piece
of the carriage ; it passes through an aperture formed in the middle of the upper
cross piece, and terminates in h by an auger or other boring tool suited to the
operation. The iron cylinder gh carries a puliey m, at a point nearly equi-
distant from the upper and lower cross pieces of the carriage.
A cord nopq is fixed to the cap in the point n, passes over the fixed puliey o
placed near the middle of one of the vertical or side frames of the carriage, passes
enti rei y round the horizontal puliey m, and afterwards over a vertical puliey p
placed opposite to the puliey o in the other side frame of the carriage, and
terminates in q, where it sustains the weight N, which operates to keep the cord
in an uniform de<rree of tension.
If the moving power act by an alternate circular movement, that movement158
may be converted into an alternate rectilinoar movement by tlie metbod already
explained in our article B 17. The iron cyiinder gh vili participate in this
alternate rcctiliuear movement of the carriage: and will at the same time have
an alternate circular movement produced by theuniform tension of the cord onpq.
The combination of these two movements will therefore communicate a spiral
movement to the boring tool, as in the subject exhibited in our article K 10.
SECTION XXI.
To convert an alternate movement in a given curve of uniform velocity, or vohich
is variable by a given late, into an alternate movement in another given curve,
of velocity similar to that of the original movement, uniform, or varying] by a
given lavo, ani in the same or in different planes of direction.
THE given alternate movement in a curve will be converted into a direct
circular movement by the methods shewn in Section IX.; and the movement
so obtained, into an alternate movement in the curve required by the examples
of the same Section.
Those movements which are adapted to the solution of the problems stated
in Section XIV, will also apply to this Section.
THE ENO.ALPHABETICAL INDEX
A.	Page.
Auxiliary piate, explanation of	2
A X, explanation of the subject	4
A 2,--------------—----------- 10
A 3,----------------------- 12
A 4,-----------------------28
Archimedean screw, appiication of	26
Alternate circular motion, by a yessel at
single anchor	29
A 7, explanation of	the	subject	31
Auger, M. his movement for pump pistons 36
A 7', explanation of the subject	46
Adjustraent of an upper mill stone	66
A 8, explanation of the subject	73
Anemometer by Leupold	86
A 9, explanation of	the	subject	91
A 9',------------------------- 106
Alix, M. his machine for drawing loads	100
Amant, M. his dead beat watch escapement 106
Arnold, his free watch escapement	107
A 10, explanation of	the subject	117
A 14, --------------------------------------135
Autograph, mention of	136
A 17, explanation of	the subject	137
A 19,----------------------153
A 20,------------------------- 155
B.
B 1, explanation of the subject	4
Bossut, his corn mill	9
B 5, explanation of the subject	12
Borda, his memoir on hydrauiic wheels	15
B 4, explanation of the subject	28
Boitias, his hydrauiic clock movement	30
B 7, explanation of the subject	32
Page.
Bockier, his method of converting direct cir-
cular motion into alternate rectilinear	38
Butuing, his calendering engine	40
B 7', explanation of the subject	46
Bettancourt, his machine for cleansing har-
bours	55
------------his machine for the conversion
of direct circular motion, into alternate
rectilinear motion	64
Branca, Ilis method for ditto	ibid
Bucket engine for raising water, by M. Bet-
tancourt	ibid
Bockier, his method of adjustment for the
stones of a mill	67
Breguet, his improvements in watch making 74
B 8, explanation of the subject	79
Bettancourt and Breguet, their appiication
of methods for changing the direction of
circular motion	87
Breguet, his methods of equalizing the action
of first movers	89
B 9, explanation of the subject	91
Bucket engine for raising water, by Leupold 92
Bingen, his rotatory motion	94
Breguet, his equatorial clock	98
Bockier, a method of his for working pumps 100
B 9;, explanation of the subject	107
Breguet, his remonicire watch escapement 109
-------- his remonfoire ckck escapement 111
Berthoud, his free escapement	107, 108
B 10, explanation of the subject	118
B 14,--------------------------------------- 136
B 17,--------------------------------------- 137
B 19,--------------------------------------- 153
B 20,--------------------------------------  155ALPIIABETTCAL INDF.X.
c.	Page.
Classification of first movers	O i>
C 1, explanation of the subject	4
Coni mill by Bossut and Solage	9
Centrifugal machine by Mour	12
C 3, explanation of the subject	ibid
Cagniard Latour, his hydraulic engine	26
Crab engine	27
Clock movement, by Perrault	28
. 		, hydraulic, by Boitias	46
C 4, explanation of the subject	29
C 7,		33
Cylinder of variable diameter	ibid
Churn, movement for	40
Calendering engine, movement for	ibid
Crank movements	46
C 7', explanation of the subject	47
Checks, on the application of, to machinery	
	48—59
Crane, reference to one, by Pinchbeck	53
Camus, M. his engine for driving piles	55
Cardinefs machine for an horizonta! rotatory	
motion for purposes of amusement	70
C 8, explanation of the subject	80
€9,	92
Cartwright, reference to his patent	95
Clock movements, reference to	97, 98
Clock, equatoriai, by Breguet	98
Clock and Watch escapements, descriptive	
classification of	102, 103
Crown wheel escapement	104
Clement, his escapement	105
Cylinder escapement of Graham	ibid
C 9', explanation of the subject	108
Compasses for describing curvilinear	and
spiral figures	124
C 17, explanation of the subject	138
Curves, mechanical description of them	i 119
Camus, his bolting machine	153
C 19, explanation of the subject	154
C 20,		156
D.
D 1, explanafion of the subjoct	5
D 3,-------------------------- 14
Page.
Dutch mill, doscription of	19
D 4, explanafion of the subject	29
D 7,---------------------------- 34
De Caus, his hydraulic engine referred to 41
D 7', explanafion of the subject	47
Dcraching the working parts of a machine
from the mover, observations on	48, 49
Dubuisson, his machine for pounding plaster 58
Ddaching auimal first movers, method of, by
M. Prony	68
D 8, explanafion of the subject	80
Droz, his flatting engine referred to	87
D 9, explanation of the subject	92
Dead beat escapement	102
D 9', explanation of the subject	109
D 10,---------------------------------------- 121
Double piston pump,	by	Berger	138
Drill	143
Driil bow	145
D 19, explanation of the subject	154
D 20,---------------------------------------  156
E.
Explanation of the Synoptical	table	1, 2
E 1, explanation of the subject	5
E 3,-------------------------- 15
E 4,--------------------------■	29
E 7,------------------*------- 34
E 7',------------------------- 55
Endless Screw, application of	80
E 8. explanation	of the	subject	ib.
Equalization of the action of first movers,
by Breguet	89
E 9, explanation	of the	subject	93
Equatoriai clock, by Breguet	98
E 10, explanation of the subject	125
Engine for cutting screws, description of 132
----------------- fusees, ditto	ibid
E 17, explanation of the subject	142
Escapement, by Volet	92
------------? classification of the various 102, 103
------------, the crovvn wheel	104
------------, the dead beat for seconds, by
G rabam	ibidALPHABETICAL INDEX.
Pago.
Escapcment, the dead beat cylinder,	for
watches, by Diito	105
> —.....——, the dead beat, by Amant	106
------------? the free, by Arnold	107
-------------------9 by Berthoud	108
.-----------, the free remontoire, by Haley 109
-------------the	remontoire, by Breguet	ibid
Eccentricity of the planetary orbits, machine
for exhibiting it	85
E 9*, explanation of the subject	111
Ellipsograpl.s, references to	125
E 19, explanation of the subject	1
F.
F 1, explanation of the subject	5
F 3,-------------------------- 15
F 7,-------------------------- 35
Fly wheel, Cartwrighfs	47
F 7f, explanation of the subject	56
First movers, classification of	3
--------— machine for suspending the
action of, by Prony	62
----■-------method of detaching animals from
the working parts of a machine,
when so used	63
•-----------method of equalizing by Breguet 89
Force of the wind, machine for indicating it,
by Leupold	86
Flatting engine, by Droz	87
F 8, explanation of the subject	81
F 9,----------------------------------------- 93
Fuiton, his patent for a method of working
pumps	91
F 9', explanation of the subject	H3
FIO,-----------------------—	126
Fusees, engine for cutting them	132
F 17, explanation of the subject	143
Franklin, his double piston pump	ibid
F 19, explanation of the subject	1
G.
G 1, explanation of the subject	6
G 3, —---------------------------------------  15
G 7, --------------—---------- 38
G 7',----------------------------------------   58
Page.
G 8, explanation of fhe subje ct	81
G 9,----------------------------- 94
Garousse M. his levers	99
G	9',	explanation	of the	subject	114
G	10,--------------------------- 127
Geometric pen, description	of	129
G	17,	explanation of the	subject	143
Gun barrels, method of rifling, by Jacquet,
referred to	63
---in the manufac.
tories of Versailles
H.
H 1, explanation of the subject	6
Hydraulic ram, of Montgolfier	7
--------------spiral,	15
H 3, explanation of the subject	ibid
Hydraulic wheels, memoir on them by
M. Borda	15, 16, 17, 13
■	wheel, of M. Mannoury d’Ectat 24
Horizontal windmill	ig
Hydraulic machine, of Cagniard Latour	26
*——-------clock movement, by Perrault	28
--------------------------by Boitias	30
H 7, explanation of the subject	39
Hydraulic engine, by De Caus	41
Harbours, machine for cleansing, by M.
Bettancourt	55
H 7', explanation of the subject	58
Hydraulic machine of Marly, report on the
re-establishment of	ibid
H 8, explanation of the subject	gi
H 9,-----------------------------------------94
H 9',---------------------------------------114
H 10,-------------------------------------- igg
H 17,-------------------------------------- 143
Hygrometer, by Leupold	127
Henry, his machine for raising weighis	100
Haley, his remontoire eseapement	109
X.
I 1, explanation of the subject	7
I 3,-------------------------------------    18
I 7,-----------------------------------------40
I 7',--------------------------------------- 59
yALPHABET1CAL INDEX.
Page.
I 8, explanatiori of the subject	82
I 9,----------------------------------------------95
I 9',--------------------------------------------116
I 10,------------------------------------------  129
I 17,------------------------------------------- 144
K.
K 1, explanation of	the	subject	7
K 3,------------------------20
K 7,------------------- ------ 40
R 7',----------------------- 62
K 8,------------------------83
K 9,------------------------96
K 9',-----------------------116
K 10,-----------------------131
K 17,---------------------- 145
L.
L 1, explanation of	the	subject	8
L 3,------------------------23
L 7,-------------------------- 41
Leslie, his tide mill	67
L 8, explanation of	the	subject	85
L 9,------------------------97
L 10, —-------------------- 131
Leupold, his movement for pump pistons 34
-	........, his methods of converting direct
circular motion into alternate
rectilinear	36, 37
-----------,	his anemometer	86
.---------,	his bucket engine for raising water	92
-	-----*,	his hygrometer	127
Levers, by	Garousse	99
L 17, explanation of the subject	146
M.
^Jlfannoury d’Ectot, M* Ie Marquis, his ma-
chine	10
Mour, his centrifugal machine	12
Mill, reference to one used in Holland	19
Mill-stones, method of adjusting them	66—77
Mirrors, machine for polishing them	79
Montgoitier, his hydraulic ram	7
Machine of Segne r	12
- —- for sawing stone	40
•-------- ——- ■ - " ■ marbie	ibid
Page.
Machine for ribbon weaving	40
-	....- for raising masses of stone from the
quarry	52
------- for cleansing harbours by M. Bet-
tancourt	55
-------for pounding plaster	58
—	------ of Marly, report on the re-esta-
blishment of it	ibid
------- of White, description of it	59
------- for the conrersion of direct circular
motion into alternate rectilinear,
by M. Bettancourt	65
•------------------------, by M. Branca ibid
-------- for an horizontal rotatory motion,
by M. Cardinet	70
-------- for polishing watch springs, by
Thiout	72
-----— for pounding the component mate-
rials of porcelain	77
------- for polishing mirrors, by Sureda 79
------- for changing the direction of circu-
lar motion	87
--------------------------------------, ap-
plication of it, by De Bettan-
court and Breguet	ibid
for drawing loads, by M. Alix	100
------- for grinding and polishing mirrors 131
------- for cutting piles under water	138
-------- for exhibiting the eccentricity of
the planetary orbits	85
------- for raising sunken vessels	138
Mechanisro, applicable to rose engine turning 120
-----------producing the sustaining power
in w&tches	111
M 3, explanation of the subject	24
M 7,------------------------------------------42
M 7',---------------------------------------- 64
M 8,------------------------------------------85
M 9,------------------------------------------98
M 10, -----—---------------------------------132
Micrometrical adjustment, a screw for, by
M. Prony	14
M 17, explanation of the subject	146ALPHABETICAL INDEX.
N.	Page.
Nut and screwr, properties of	12, 13
Noble, Mr. his pump	139
N 3, explanation of the subject	24
N 7,----------------------------------------- 43
N 7',---------------------------------------  66
N 8,----------------------------------------- 86
N 9, ---------------------------------------- 99
N 10,--------------------------------------- 134
N 17,--------------------------------------- 146
O.
Otfershot wheels	17
O 3, explanation of the subject	26
O 7, —*-------------------------------------  43
O 7f,---------------------------------------- 67
O 8,------------------------------------------87
O 9,---------------------------------------   99
O 17,--------------------------------------- 148
P.
Parallel motion	5
----------------by	parallel roilers	6
----------------by	reversed wedges	ibid
—	--- ruler	7
Pyrometrical	movers	9
Perrault,	his	clock movement	28
--------engine	for raising weights	29
Pump pistons, a movement for, by M. Auger 36
Piedmont, silk-mill of	80
Pumps, Fulton’s patent for a method of
working them	91
-------methods of working	by	Bockler	100
----------------------------by Ramelli 101
—	■	one by Noble	139
—	--a double piston,	by	Berger	138
■------------------------- by Franklin	143
Pantograph, description of	136
Piles, machine for cutting them, under water 138
Prony, his micrometrical adjusting screw	14
—	..his method of detaching animal first
movers from the working parts of
machine ry	68
Pile engine, by M. Camus	55
P 3, explanation of the subject	27
P 7,------------------------------------------ 44
Page.
P 7', explanation of the subject	69
P 8,------------------------- 88
P 9,-------------------------100
P 17,------------------------------------    149
Q.
Q 7, explanation of the subject	44
Q7',------------------------- 71
Q 8, ---------------------------------------  88
Q 9,---------------------------------------- 100
R.
Ram, hydraulic, of Montgolfier	7
Ribband weaving, machine	for	40
Rose engine turning, mechanism applicable to 120
R 7, explanation of the subject	45
R7',------------------------- 72
R 8,----------------------------------------  89
R 9,---------------------------------------  100
Rotatory motion, an horizontal one by
Cardinet	70
----------------by Bingen	94
Ramelii, his applicadon of certain movements
to working pumps	101
Raising water, engine for, by M. Bettancourt 64
Roemer M. his mechanism for cxhibiting the
eccentricity of the planetary motion	85
Regulating mechanism, to correct the inequa-
lities of the moving power	88
Raising water, machine for, by Leupold	92
Rotatory motion, by Cartwright	95
Raising weights, machine for, by M.	Henry 100
S.
Segner, his machine dcscribed	12
Spiral, the hydraulic	] 5
Steam-engine, of M. Verzy	23
Sawir.g marble, machine for	40
-------stone------------------------------ ib,*d
Silk reel, an ltalian	43
Siik mill, of Piedmont, descripdon	of	80
Screw, endless, applicadon of	ibid
Spiral compasses, descripdon of	]o4
Spiral lines, method of describing them on
rylindrical surfaces	jog
Screws, engine for cuttirsg	132
1ALPHABETICAL INDEX.
Page.
Sunken vessels, machrne for raising them	138
Syncptical piate, explanation of	1, 2
S 7', explanation of the subject	72
S 8,----------------------------------------- 90
S 9,-----------------------------------------104
Sustaining power, on the preservatioa and
communication of it	111
T.
Tide mill, by Leslie	67
Turning, mechanism applicable to	120
T7', explanation of the subject	72
Telegraph, application of the universal joint
toits mechanism, by Bettancourt and
Breguet	87
T 9, explanation of the subject	104
U.
Universal w indmill	24
U 7, explanation of the subject	44
Universal joint for effecting a change in the
directlon of mechanical movements	87
U 9, explanation of the subject	105
W.
Windmills, horizontal	18
-----------with vertical sails	20
-----------universal	24
Wind gage, by Leupold	86
Watch escapcment, by Volet	93
X.
Y,
Zureda, reference to his carding machine 34
———his mechanism for converting rotatory
motion into alternate reetiUnear 4 )
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