The Dividing Engine

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The following article by Anthony A. Leiserowitz is taken from the Museum of Surveying Newsletter

The Dividing Engine in History


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Circular Dividing Engine that made surveying and scientific instruments sold by the Berger Company.  This wonderful machine is on exhibit at the Museum of Surveying in Lansing, Michigan

In 1773, Jesse Ramsden of England invented the circular dividing engine, an instrument which had a profound impact on Western history.  Prior to his invention, the division and inscription of scales on mathematical instruments was done by hand.  Therefore, the value of the instrument depended on the accuracy of the maker and his tools.  Instruments such as surveying compasses were subject to wide variations in quality, as each instrument required a maker with an extraordinary control of tools and a very precise eye.  Instruments were produced one at a time, which limited the number available for purchase and making them prohibitively expensive.

Ramsden's invention of the mechanical dividing engine, however, eliminated human error and increased the production of precise scientific and mathematical instruments.  This was particularly important for the development of the octant and the sextant, both vital to the British Navy.  These instruments made the exploration of the world's oceans and the establishment of the British Empire possible.  An octant or sextant enabled a sea captain to determine longitude, which, when mapped against latitude, provided his precise location anywhere on Earth.  Ramsden shared in the national prize given to solve the longitude measurement problem.

For several decades, the British dominated the trade in precise instruments, as no American could compete with the new products of the mechanical dividing engine.  "The first American instrument maker known to have developed [the] capability for mechanical graduation of instruments was William J. Young, who specialized in the production of surveying instruments...In the early 1830's Young undertook a larger dividing engine to be used for more precise work, claiming to have introduced an important new principle, and later he modified the engine further so that it was automatically operated.  Finally, some years later, he constructed a circular dividing engine having  a radius of 48 inches, which remained unequaled in the United States for some time.  Young used it for graduating the scales of engineers' transits and of astronomical instruments.  The most successful of Young's endeavors, it was capable of dividing circular scales 44 inches in diameter." (Bedini, pp. 369-370)

This was quite an accomplishment for his time.  According to a reported extract from the proceeding of the Meeting of Instruments of Precision, before the Society of Arts at Massachusetts Institute of Technology in 1877, "There is no branch of mechanical arts which require more skill in the use of tools, more geometric knowledge, or greater patience, than the construction of an automatic dividing engine." (Whitelaw, p. 4)

The precise instruments made by Young's dividing engines were crucial to the surveying profession as the growing United States began to explore and colonize the American West.  The dividing engine not only made the surveyor's compass more accurate, but also helped it evolve into more sophisticated instruments.  As railroads were laid across the United States, surveyors found they needed an instrument which would allow them to "determine a number of angles in less time and more accurately than was possible with the plain or vernier compass.  The railroad compass was equipped with a vernier reading inside the compass dial.  The surveyor's transit was [then] evolved by the addition of a telescope to replace the sighting bars.  The telescope enabled the horizontal and vertical angles of an objective to be measured simultaneously with reference to an assumed horizontal plane and assumed azimuth direction.  The outstanding feature of the transit which made it an improvement over the theodolite was that its telescope could be "transited," or completely revolved on its horizontal axis.   Shortly after the instrument was first commercially produced in quantity in about 1830 by William J. Young, it achieved international use and has survived with virtually little change until the present."  (Bedini, pp. 370-371)

In 1856, at the age of 14, Christian Louis Berger began a decade of apprentice work with some of the finest manufacturers of precision mathematical and astronomical instruments in Europe.  In 1866, he emigrated to the United States and spent an additional five years working for American instrument makers.  Finally, on October 18, 1871, he and George L. Buff established the firm of Buff and Berger, specializing in surveying, engineering, mining, and scientific instruments.  The company was very successful until 1898, when the two founders dissolved the firm after a dispute over how to apportion the business among their sons.

C. L. Berger and his two sons acquired all the assets of Buff and Berger, moved the company to 37 Williams Street in Roxbury, Massachusetts, and made instruments for civil, geodetic, geological and petroleum engineers and surveyors around the world.  They also diversified to produce special and unique instruments for scientists and particularly astronomers.  It is suggested that even Albert Einstein visited their factory looking for precise astronomical instruments.  (Whitelaw, p. 5)

Equipped with a set of excellent dividing engines, this period was arguably Berger Instrument's most productive and influential, and led to its association with academia and the publication of its unique and comprehensive catalogues."  (Whitelaw, p. 4)  The company continued after the death of C. L. Berger in 1922 until it was sold in 1948.

Miraculously, Berger's dividing engines remained untouched and forgotten for the next 47 years.  In 1995, however, Chicago Steel Tape Company, owned by Mr. Dennis Nardoni, acquired the old Berger factory and discovered these historic machines.  Mr. Nardoni generously donated a Heyde Circular Dividing Engine to the Museum of Surveying in Lansing, Michigan, where it is now on display.  Known as Berger's Engine No. 5, it was built by Gustav Heyde of Dresden, Germany and purchased by Berger about 1907.  This machine is still operable and was the primary circular dividing engine in use at Berger.  (Garcelon, p. 5)   Mr. Nardoni also donated a Societe Genevoise D'Instruments de Physique Longitudinal Graduating Engine to the Museum, also on exhibition.

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The Societe Genevoise D'Instruments de Physique Longitudinal Graduating Engine 





Bedini, Silvio A.  Thinkers and Tinkers   Rancho Cordova, CA:  Landmark Enterprises, 1975

Garcelon, David C.   Appraisal Summary of the Berger Instrument Co. Graduating Engine Room, 1996

Smart, Charles E.    The Makers of Surveying Instruments in America Since 1700   Troy, NY:  Regal Art Press, 1962

Whitelaw, J. P.   The Early History of Berger Instruments, 1995





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