Keufell & Esser N 4102 Surveyor's

The N 4102 Surveyor's Duplex was produced by K&E since 1915 until 1949. As well as the other K&E rules of that time, it was fabricated with Mahogany wood covered with white celluloid where scales were engraved, and hold with brass braces. Cursor in the first models was frameless, and by the second half of the 1930's was equiped by the traditional wireframed. With an initial cost of $18.00 USD (About $532 USD in 2022), it was designed to tackle some of the difficult astronomical calculations requiered during surveying. As stated in the 1915 product catalog:

The fact that all astronomical data essential to surveying, such as azimuth, time, latitude, etc. can be ascertained by means of the usual type of Transit with vertical but without solar attachment, while generally known, is rather seldom utilized in this country. The main reason for this surprising condition is the difficulty of computing, in the field of spherical trigonometry, the resultso of the observations.

The new K&E Surveyor's Rlide Rule enterely eliminates this difficulty by reducing the hitherto complicated calculations to more machanical oprations, thereby rendering the method of field astronomy with the regular Engineering's Transit extremely simple and practical.

The scales on the N 4102 are: Front: Vert 1/2 sin2a (55' - 4^o 37'), A, B, CI, C, D, Vert 1/2 sin2a - HOR cos²a. Back: D, sin d (folded), cos l & h, C, tan (5^o 44' - 45^o), tan I, Az (double). The precision achieved in the N 4102 for the trigonometric calculations is of 1 minute of arc.

Besides the regular A, B, CI, C and D scales for general calculations, the N 4102 has the next specialized scales:

• sin d: folded scale (at 5^o 44' ), from 2^o 22' - 24^o 44' , used for declination.

• cos l and h, inverted scale, from 0^o to 84^o 15', for latitude and altitude

• tan I , inverted scale, from 20^o 50' to 75^o

• Az, Azimuth double scale or scale of natural cosines, for reading azimuth or cosine bearings, from 0^o to 60^o (inverted upper scale), and from 50^o to 100^o (lower scale)

• HOR 1/2 cos²a, inverted scale, from 0^o to 45^o , to calculate horizontal distance

• VERT 1/2 sin2a, splitted scale, one portion from 29.9' to 5^o 45', and the second portion from 5^o 45' to 40^o , to calculate vertic;al distance

According with the serial number engraved on the specimen in this collection (598512), and the correlation done by Ed Chamberlain, this rule was fabricated around 1935, and was sold for $24 USD (about $522 in 2020 USD)

References:

• Smith Richard H - McCoy Clark: K&E 4102 Surveyors Duplex Slide Rule. Journal of the Oughtred Society. Volume 18, Number 2, Fall 2009 pp. 40-45 https://osgalleries.org/journal/pdf_files/18.2/V18.2P40.pdf

• Van Poelje, O.E. : Stadia or Tachymetrical Slide Rules. UKSRC Gazette Nr. 6, August 2005. https://www.rechenschieber.org/stadia.pdf