A dividing engine is a device specifically employed to mark graduation

Graduation (instrument)

-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 ruler

Ruler

A ruler, sometimes called a rule or line gauge, is an instrument used in geometry, technical drawing, printing and engineering/building to measure distances and/or to rule straight lines...

 or vernier

Vernier scale

A 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 protractor

Protractor

In 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...

, astrolabe

Astrolabe

An astrolabe is an elaborate inclinometer, historically used by 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 longitude, surveying, triangulation, and to...

, sextant

Sextant

A sextant is an instrument used to measure the angle between any two visible objects. Its primary use is to determine the angle between a celestial object and the horizon which is known as the altitude. Making this measurement is known as sighting the object, shooting the object, or taking a sight...

, theodolite

Theodolite

A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...

, or setting circles

Setting circles

Setting 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 wood

Wood

Wood is a hard, fibrous tissue found in many trees. It has been used for hundreds of thousands of years for both fuel and as a construction material. It is an organic material, a natural composite of cellulose fibers embedded in a matrix of lignin which resists compression...

, ivory

Ivory

Ivory is a term for dentine, which constitutes the bulk of the teeth and tusks of animals, when used as a material for art or manufacturing. Ivory has been important since ancient times for making a range of items, from ivory carvings to false teeth, fans, dominoes, joint tubes, piano keys and...

 or brass

Brass

Brass is an 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...

. 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 quadrants

Quadrant (instrument)

A quadrant is an instrument that is used to measure angles up to 90°. It was originally proposed by Ptolemy as a better kind of astrolabe. Several different variations of the instrument were later produced by medieval Muslim astronomers.-Types of quadrants:...

 and astrolabe

Astrolabe

An astrolabe is an elaborate inclinometer, historically used by 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 longitude, surveying, triangulation, and to...

s in the 15th and 16th centuries did not show fine graduations and were relatively roughly made.

In the 16th 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 masters

Master craftsman

A 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....

.

Transversal

Transversal (instrument making)

Transversals 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 14th century. Tycho Brahe

Tycho Brahe

Tycho 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 Hire

Philippe de La Hire

Philippe 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 16th century by Pedro Nunes

Pedro Nunes

Pedro Nunes , was a Portuguese mathematician, cosmographer, and professor, from a New Christian family. Nunes, considered to be one of the greatest mathematicians of his time , is best known for his contributions in the technical field of navigation, which was crucial to the Portuguese period of...

 and was called nonius after him. It consisted of tracing a certain number of concentric

Concentric

Concentric 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 Brahe

Tycho Brahe

Tycho 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 Clavius

Christopher Clavius

Christopher 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 Vernier

Pierre Vernier

Pierre 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 scale

Vernier scale

A 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 gear

Gear

A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine....

 cutting machines had prepared the way. Such devices were required to cut a circular plate with uniform gear teeth

Gear

A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine....

. Clockmakers were familiar with these methods and they were important in developing dividing engines. George Graham

George Graham (clockmaker)

George Graham was an English clockmaker, inventor, and geophysicist, and a Fellow of the Royal Society.He was born to George Graham in Kirklinton, Cumberland. 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 Bird

John Bird (astronomer)

John 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...

 and Jeremiah Sisson followed on with these techniques. These beam compass techniques were used into the 19th 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 Hindley

Henry Hindley

Henry 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 Smeaton

John Smeaton

John Smeaton, FRS, was an English civil engineer responsible for the design of bridges, canals, harbours and lighthouses. He was also a capable mechanical engineer and an eminent physicist...

 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 Ramsden

Jesse Ramsden

Jesse Ramsden FRSE was an English astronomical and scientific instrument maker.Ramsden was born at Salterhebble, Halifax, West Riding of 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...

 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 lathe

Screw-cutting lathe

A 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 Longitude

Board of Longitude

The 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 administer a scheme of prizes intended to encourage innovators to solve the problem of finding longitude at sea.-Origins:Navigators and...

 on condition that it was described in detail (along with the related screw-cutting lathe

Screw-cutting lathe

A 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 Troughton

Edward Troughton

Edward Troughton FRS was a British instrument maker who was notable for making telescopes and other astronomical instruments.Troughton was born at Corney, Cumberland...

 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 Lenoir

Etienne Lenoir (instrument maker)

Etienne 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 19th century, it was possible to make instruments such as the sextant

Sextant

A sextant is an instrument used to measure the angle between any two visible objects. Its primary use is to determine the angle between a celestial object and the horizon which is known as the altitude. Making this measurement is known as sighting the object, shooting the object, or taking a sight...

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.