A
dividing engine is a device specifically employed to mark
graduation-Linear graduation:Linear graduation of a scale occurs on a straight instrument. The graduation can identify linear measures, such as inches or millimetres on a rule. They can also be non-linear such as logarithmic or other transcendental scales....
s on measuring instruments.
There has always been a need for accurate measuring instruments. Whether it is a linear device such as a
rulerA ruler, or rule, is an instrument used in geometry, technical drawing and engineering/building to measure distances and/or to rule straight lines. Strictly speaking, the ruler is essentially a straightedge used to rule lines and the calibrated instrument used for determining measurement is called...
or
vernierA vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale...
or a circular device such as a
protractorIn geometry, a protractor is a circular or semicircular tool for measuring an angle or a circle. The units of measurement utilized are usually degrees.Some protractors are simple half-discs; these have existed since ancient times...
,
astrolabeAn astrolabe is a historical astronomical instrument used by classical astronomers, navigators, and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets, and stars; determining local time given local latitude and vice-versa; surveying; and...
,
sextantA sextant is an instrument generally used to measure the altitude of a celestial object above the horizon. Making this measurement is known as sighting the object, shooting the object, or taking a sight. The angle, and the time when it was measured, can be used to calculate a position line on a...
,
theodoliteA theodolite is an instrument for measuring both horizontal and vertical angles, as used in triangulation networks. It is a key tool in surveying and engineering work, particularly on inaccessible ground, but theodolites have been adapted for other specialized purposes in fields like meteorology...
, or
setting circlesSetting circles are used on telescopes equipped with an equatorial mount to find astronomical objects in the sky by their equatorial coordinates often used in star charts or ephemeris.-Description:...
for astronomical telescopes, the desire for ever greater precision has always existed. For every improvement in the measuring instruments, such as better alidades or the introduction of telescopic sights, the need for more exact graduations immediately followed.
In early instruments, graduations were typically etched or scribed lines in
woodWood is an organic material; in the strict sense wood is produced as secondary xylem in the stems of trees . In a living tree it transfers water and nutrients to the leaves and other growing tissues, and has a support function, enabling woody plants to reach large sizes or to stand up for themselves...
,
ivoryIvory is formed from dentine and constitutes the bulk of the teeth and tusks of animals such as the elephant, hippopotamus, walrus, mammoth and narwhal....
or
brassBrass is any alloy of copper and zinc; the proportions of zinc and copper can be varied to create a range of brasses with varying properties. In comparison, bronze is principally an alloy of copper and tin. Despite this distinction, some types of brasses are called bronzes. Brass is a...
.
A
dividing engine is a device specifically employed to mark
graduation-Linear graduation:Linear graduation of a scale occurs on a straight instrument. The graduation can identify linear measures, such as inches or millimetres on a rule. They can also be non-linear such as logarithmic or other transcendental scales....
s on measuring instruments.
History
There has always been a need for accurate measuring instruments. Whether it is a linear device such as a
rulerA ruler, or rule, is an instrument used in geometry, technical drawing and engineering/building to measure distances and/or to rule straight lines. Strictly speaking, the ruler is essentially a straightedge used to rule lines and the calibrated instrument used for determining measurement is called...
or
vernierA vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale...
or a circular device such as a
protractorIn geometry, a protractor is a circular or semicircular tool for measuring an angle or a circle. The units of measurement utilized are usually degrees.Some protractors are simple half-discs; these have existed since ancient times...
,
astrolabeAn astrolabe is a historical astronomical instrument used by classical astronomers, navigators, and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets, and stars; determining local time given local latitude and vice-versa; surveying; and...
,
sextantA sextant is an instrument generally used to measure the altitude of a celestial object above the horizon. Making this measurement is known as sighting the object, shooting the object, or taking a sight. The angle, and the time when it was measured, can be used to calculate a position line on a...
,
theodoliteA theodolite is an instrument for measuring both horizontal and vertical angles, as used in triangulation networks. It is a key tool in surveying and engineering work, particularly on inaccessible ground, but theodolites have been adapted for other specialized purposes in fields like meteorology...
, or
setting circlesSetting circles are used on telescopes equipped with an equatorial mount to find astronomical objects in the sky by their equatorial coordinates often used in star charts or ephemeris.-Description:...
for astronomical telescopes, the desire for ever greater precision has always existed. For every improvement in the measuring instruments, such as better alidades or the introduction of telescopic sights, the need for more exact graduations immediately followed.
In early instruments, graduations were typically etched or scribed lines in
woodWood is an organic material; in the strict sense wood is produced as secondary xylem in the stems of trees . In a living tree it transfers water and nutrients to the leaves and other growing tissues, and has a support function, enabling woody plants to reach large sizes or to stand up for themselves...
,
ivoryIvory is formed from dentine and constitutes the bulk of the teeth and tusks of animals such as the elephant, hippopotamus, walrus, mammoth and narwhal....
or
brassBrass is any alloy of copper and zinc; the proportions of zinc and copper can be varied to create a range of brasses with varying properties. In comparison, bronze is principally an alloy of copper and tin. Despite this distinction, some types of brasses are called bronzes. Brass is a...
. Instrument makers devised various devices to perform such tasks. Early Islamic instrument makers must have had techniques for the fine division of their instruments, as this accuracy is reflected in the accuracy of the readings they made. This skill and knowledge seems to have been lost as small
quadrantNot to be confused with quartileQuadrant may refer to:* Quadrant , a measuring instrument capable of measuring angles up to 90°* In science-fiction: Galactic quadrants...
s and
astrolabeAn astrolabe is a historical astronomical instrument used by classical astronomers, navigators, and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets, and stars; determining local time given local latitude and vice-versa; surveying; and...
s in the 15
th and 16
th centuries did not show fine graduations and were relatively roughly made.
In the 16
th century, European instrument makers were hampered by the materials available. Brass was in hammered sheets with rough surfaces and iron graving tools were poor quality. There were not enough makers to have created a long tradition of practice and few were trained by
mastersA master craftsman or master tradesman was a member of a guild. In the European guild system, only masters were allowed to be members of the guild....
.
TransversalTransversals are a geometric construction on a scientific instrument to allow a graduation to be read to a finer degree of accuracy. Transversals have been replaced in modern times by vernier scales.-History:...
s set a standard in the early 14
th century.
Tycho BraheTycho Brahe, born Tyge Ottesen Brahe , was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...
used transversals on his instruments and made the method better known. Transversals based on straight lines do not provide correct subdivisions on an arc, so other methods, such as those based on the use of circular arcs as developed by
Philippe de La HirePhilippe de La Hire , was a French mathematician and astronomer. According to Bernard le Bovier de Fontenelle he was an "academy unto himself"....
, were also used.
Another system was created in the 16
th century by
Pedro NunesPedro Nunes , was a Portuguese mathematician, cosmographer, and professor, born from a New Christian family....
and was called
nonius after him. It consisted of tracing a certain number of
concentricConcentric objects share the same center, axis or origin with one inside the other. Circles, tubes, cylindrical shafts, disks, and spheres may be concentric to one another...
circles on an instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. Thus the outermost quadrant would have 90° in 90 equal divisions, the next inner would have 89 divisions, the next 88 and so on. When an angle was measured, the circle and the division on which the alidade fell was noted. A table was then consulted to provide the exact measure. However, this was a system that was difficult to construct and few used it.
Tycho BraheTycho Brahe, born Tyge Ottesen Brahe , was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...
was one exception.
Some improvements to Nunes' system were developed by
Christopher ClaviusChristopher Clavius was a German Jesuit mathematician and astronomer who was the main architect of the modern Gregorian calendar...
and Jacob Curtius. Curtius' work led directly to that of
Pierre VernierPierre Vernier was a French mathematician and instrument inventor. He was inventor and eponym of the vernier scale used in measuring devices....
, published in 1631. Vernier refined this process and gave us the
vernier scaleA vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale...
. However, these various techniques improved the reading of graduations, but they did not contribute directly to the accuracy of their construction. Further improvements came slowly, and a new development was required: the dividing engine.
Prior work on the development of
gearA gear is a component within a transmission device that transmits rotational torque by applying a force to the teeth of another gear or device. A gear is different from a pulley in that a gear is a round wheel that has linkages that mesh with other gear teeth, allowing force to be fully...
cutting machines had prepared the way. Such devices were required to cut a circular plate with uniform gear
teethA gear is a component within a transmission device that transmits rotational torque by applying a force to the teeth of another gear or device. A gear is different from a pulley in that a gear is a round wheel that has linkages that mesh with other gear teeth, allowing force to be fully...
. Clockmakers were familiar with these methods and they were important in developing dividing engines.
George GrahamGeorge Graham was an English clockmaker, inventor, and geophysicist, and a member of the Royal Society. A Friend like his mentor Thomas Tompion, Graham left Cumberland in 1688 for London to work with Tompion....
devised a process of using geometric methods to divide the limb of an instrument. He developed a sophisticated beam compass to aid marking of the graduations.
John BirdJohn Bird the great mathematical instrument maker was born at Bishop Auckland. He worked in London for Jeremiah Sisson, and by 1745 he had his own business in the Strand. Bird was commissioned to make a brass quadrant 8 feet across for the Royal Observatory at Greenwich, where it is still preserved...
and Jeremiah Sisson followed on with these techniques. These beam compass techniques were used into the 19
th century, as the dividing engines that followed did not scale up to the largest instruments being constructed.
The first true circular dividing engine was probably constructed by
Henry HindleyHenry Hindley was an 18th century clockmaker and maker of scientific instruments. He was the inventor of a screw-cutting lathe. He built a clock for York Minster, England, where he apparently lived for much of his life, in 1752....
, a clockmaker, around 1739. This was reported to the Royal Society by
John SmeatonJohn Smeaton,
FRS, was an English civil engineer – often regarded as the "father of civil engineering" – responsible for the design of bridges, canals, harbours and lighthouses. He was also a more than capable mechanical engineer and an eminent physicist. He was...
in 1785. It was based directly on a gear cutting machine for clockworks. It used a toothed index plate and a worm gear to advance the mechanism. Duc de Chaulnes created two dividing engines between 1765 and 1768 for dividing circular arcs and linear scales. He desired to improve on the graduation of instruments by removing the skill of the maker from the technique where possible. While beam compass use was critically dependent on the skill of the user, his machine produced more regular divisions by virtue of its design. His machines were also inspired by the prior work of the clockmakers.
Jesse RamsdenJesse Ramsden was an English astronomical and scientific instrument maker.Ramsden was born at Salterhebble near Halifax, West Yorkshire, England. After serving his apprenticeship with a cloth-worker in Halifax, he went in 1755 to London, where in 1758 he was apprenticed to a mathematical...
followed duc de Chaulnes by five years in the production of his dividing engine. As with the prior inventions, Ramsden's used a tangent screw mechanism to advance the machine from one position to another. However, he had developed a
screw-cutting latheA screw-cutting lathe is a machine capable of cutting very accurate screw threads via single-point screw-cutting, which is the process of guiding the linear motion of the tool bit in a precisely known ratio to the rotating motion of the workpiece...
that was particularly advanced and produced a superior product. This engine was developed with funding from the
Board of LongitudeThe Board of Longitude was the popular name for the Commissioners for the Discovery of the Longitude at Sea. It was a British Government body formed in 1714 to solve the problem of finding longitude at sea.-Origins:...
on condition that it was described in detail (along with the related
screw-cutting latheA screw-cutting lathe is a machine capable of cutting very accurate screw threads via single-point screw-cutting, which is the process of guiding the linear motion of the tool bit in a precisely known ratio to the rotating motion of the workpiece...
) and was not protected by patent. This allowed others to freely copy the device and improve on it. In fact, the Board required that he teach others to construct their own copies and make his dividing engine available to graduate instruments made by others.
Refinements to the Dividing Engine
Edward TroughtonEdward Troughton was a British instrument maker born in Corney, Cumberland who was notable for making telescopes and other astronomical instruments....
was the first to build a copy of the Ramsden design. He enhanced the design and produced his own version. This permitted an improvement in the accuracy of the dividing engine.
Samuel Rhee developed his own endless screw cutting machine and was able to sell them to others. His screws were considered the finest available at the time.
In France,
Étienne LenoirEtienne Lenoir was a French scientific instrument maker and inventor of the repeating circle.When hired by Jean-Charles de Borda around 1772 to work on the reflecting circle, he was about thirty years old and nearly illiterate. However, his intelligence and mechanical genius allowed him to...
created a dividing engine of greater accuracy than the English version. Mégnié, Richer, Fortin and Jecker had also built dividing engines of considerable quality.
By the beginning of the 19
th century, it was possible to make instruments such as the
sextantA sextant is an instrument generally used to measure the altitude of a celestial object above the horizon. Making this measurement is known as sighting the object, shooting the object, or taking a sight. The angle, and the time when it was measured, can be used to calculate a position line on a...
that remained fully servicable and of sufficient accuracy to be in use for a half-century or more.
The dividing engine was unique among developments in the manufacture of scientific instruments, as it was immediately accepted by all makers. There was no uncertainty in the value of this development.