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![]() ![]() ![]() ![]() ![]() Cylindrical (Drum) & Spiral Calculators |
KEEP ISRM FREE! Donations are tax deductable |
This page contains cylindrical slide rules constructed in the shape of a drum and can incorporate linear or spiral (helical) scales in their design. Some images provided by major museums and private collections. Some specimens are duplicated in other galleries.
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Originally: Julius Billeter Rechenwalze. Gallery includes specimen by son Ernest Billeter Julius Billeter (1828 - 1914) made 'Rechenwalze' (Computing Rollers) cylindrical slide rules for the financial industry based on Billeter's 1894 patent. US Patent No. 513,172 January 23, 1894. French Patent No. 217,367 Nov. 10, 1891. Most of the designs were marked as "System Billeter". |
![]() National Rechenweize "System Billeter" Modell No 20 - 1918 Cylindrical Slide Rule ISRM 13.03.15.01.X
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National Rechenweize System Billeter Modell No20 1918 Cylindrical Slide Rule (Computing Roller) Made in Switzerland by National Rechenwalzen. Zurich, Switzerland. c1940, Construction: Varnished paper scales on 20.5cm (8.12in) dia. x 57.3cm (22.5in) long metal cylinder and on sliding cylindrical cage. Metal support stand. Scale: 80 sections of C & D scales equivalent to 20 meters (65.6 ft) in length. As part of the artifact, the wooden box is present that it was shipped in when it was sent from Zurich to New York City in 1940.
A record search shows that he attended U of R between 1903-1908 and that he had his own company, as General Manager of Radu Surgical Instrument Co. during the same time from 1907-1911. Then he was superintendant of the German Insurance Building, in Rochester, starting in 1911. In 1920 he was approved to be an assistance teacher (Instrument making) for high schools and appointed to Stuyvesant (NY Times Jan 30,1920).One can see why he liked this slide rule. More info on his career was in a donation to UofR in 1947 in his name that shows a more detailed work history (see attached). There is a reference that he married Clara Louise Coit who was an Alumnae class of 1897 Elmira College. She was Robert Ecker's Mother's Mother. |
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![]() REF Billeter Rechenwalze 4M Cylindrical Slide Rule |
Billeter Rechenwalze 4M Cylindrical Slide Rule Made in Switzerland by Julius Billeter. Zurich, Switzerland c1900, Construction: Varnished paper scales on 5-cm dia. metal cylinder and on metal vanes on a sliding cylindrical sleeve. Wood support stand Scale: 20 rows of C & D scales equivalent to 4 meters in length Note: This is an early example matching Billeter's 1894 patent. Later examples carry "National Rechenwalze - System Billeter" Archive - Ed Chamberlain Collection |
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![]() REF National Rechenwalzen System Billeter Modell No8 Cylindrical Slide Rule |
National Rechenwalzen System Billeter Modell No8 Cylindrical Slide Rule Made in Switzerland by National Rechenwalzen. Zurich, Switzerland c1900, Construction: Varnished paper scales on metal cylinder (8 cm dia. x 16 cm long) and on metal vanes on a sliding cylindrical sleeve. Metal support stand. Scale: 40 rows of C & D scales equivalent to 8 meters in length. Note: Formerly Julius Billeter Rechenwalze. Frequently used by European banks and accounting offices. Archive - Ed Chamberlain Collection |
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![]() REF National Rechenwalzen System Billeter Modell No16 Cylindrical Slide Rule |
National Rechenwalzen System Billeter Modell No16 Cylindrical Slide Rule Made in Switzerland by National Rechenwalzen. Zurich, Switzerlan c1910, Construction: Varnished paper scales on 16cm dia. x 36.5cm long metal cylinder and on metal vanes on a sliding cylindrical sleeve. Metal support stand. Scale: 80 rows of C & D scales equivalent to 16 meters in length. Note: Formerly Julius Billeter Rechenwalze. This cylindrical slide rule has a metal support stand that could be wall mounted. Frequently used by European banks and accounting offices. Archive - Ed Chamberlain Collection |
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![]() REF National Rechenwalze System Billeter Modell No20 1918 Cylindrical Slide Rule |
National Rechenwalze System Billeter Modell No20 1918 Cylindrical Slide Rule Made in Switzerland by National Rechenwalzen. Zurich, Switzerlan. Alleinige Fabrikanten, Switzerland c1920, Construction: Varnished paper scales on 20.5cm dia. x 57cm long metal cylinder and on sliding cylindrical cage. Metal support stand. Scale: 80 sections of C & D scales equivalent to 20 meters in length. Note: Formerly Julius Billeter Rechenwalze. This cylindrical slide rule has a metal support stand that could be wall mounted. Commonly used by European banks for currency trading. This is a previously unknown size. The largest previously known National cylindrical slide rule had a 16-m scale length. Archive - Ed Chamberlain Collection |
![]() C.O. Browne Cylindrical "Long Scale Rule" REF |
C.O. Browne Cylindrical "Long Scale Rule" Made in Australia by C.O. Browne. , No. F.C.46 Diameter 3", length 13" closed, 18" maximum Similar construction to Fuller Cylindrical Slide Rules. The single helical scale is marked on a cylinder about 2-3/4" in diameter and 4-1/2" long. The scale makes 50 turns around the cylinder, for a total length of 413" (34 feet, or 10.5 metres). It is marked to 4 significant figures at the top end, and can be read to 1 part in 20000. The inner core of the rule is covered with tables of constants, formulae, and conversion factor Scan provided by John Wolff. Australia |
![]() GB162895A |
In 1920 Capt. Leonard Charles Bygrave of the Royal Air Force patented (GB162,865A) a slide rule design in which the scales formed helices wrapped around concentric telescoping
tubes. This allowed the scales to be made sufficiently long (nearly 8 meters) to obtain the required calculational accuracy. Bygrave's method for solving the navigational
triangle involves splitting it into two right triangles and applying Napier's rules. The required operations can then be reduced to a series of multiplications and divisions of
the trigonometric functions of the relevant angles. By suitable rearrangement these can all be written in terms of cosines and cotangents, or equivalently secants and
tangents, The Bygrave slide rule scales are the logarithms of these functions. Versions of the Bygrave slide rule were produced in Germany and Japan both for marine and
aerial use. In German versions, a mechanism that allowed the sliding scale tubes to be locked to together during calculations was introduced. See "Bygrave Scales" by Robin G. Stuart, 2014 for making your own Bygrave scales. |
![]() ![]() AML Bygrave Position Line Slide Rule Mark II REF |
AML Bygrave Position Line Slide Rule Mark II Invented by Leanord Charles Bygrave in 1921. Made in England by the Air Ministries Laboratory Bygrave scales. See Reference: "PositionLineSlideRules" By Ronald W.M. Riet ©2008" Archive - Smithsonian Air And Space Museum, Science Museum of London. ![]() ![]()
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![]() ![]() AML Bygrave Position Line Slide Rule Mark IIA REF |
AML Bygrave Position Line Slide Rule Mark IIA Invented by Leanord Charles Bygrave in 1921. Made in England by the Air Ministries Laboratory Bygrave scales. See Reference: "PositionLineSlideRules" By Ronald W.M. Riet ©2008" Archive - Anderson and Garland auction ![]() ![]() ![]() |
![]() German MHR1 Bygrave Position Line Slide Rule For Navigation REF |
German MHR1 Bygrave Position Line Slide Rule For Navigation Made in Germany by Dennert & Pape.
Also See: Reference: "PositionLineSlideRules" By Ronald W.M. Riet.2008"
See A reproduction of the German MHR1 Position Line Slide Rule |
![]() REF |
Japanese WWII Navy Bygrave Position Line Slide Rule For Navigation Made in Japan - cWWII - Japanese copy of Bygrave slide rule
Also See: Reference: "PositionLineSlideRules" By Ronald W.M. Riet.2008"
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![]() K&E 4012 Thacher's Calculating Instrument REF |
K&E 4012 Thacher's Calculating Instrument Made in USA - Designed by Edwin Thacher Archive - Michael O'Leary Collection (USA) ![]() |
![]() Daemen-Schmid (Loga) 24 meter cylindrical REF |
Daemen-Schmid (Loga) 24 meter cylindrical Made in Switzerland by Daemon-Schmid 1915-1920 Paper faced aluminum drum CD (100-1000) scales divided into 60 segments for a total length of 24 meter Archive - Ed Chamberlain Collection ![]() ![]() ![]() |
![]() Loga Calculator (Daemen-Schmid) 15 meter cylindrical REF |
Loga Calculator (Daemen-Schmid) 15 meter cylindrical Made in Switzerland by Daemon-Schmid |
![]() Loga (Daemen-Schmid) 7.5 meter cylindrical ISRM (deaccessioned 11.15.2023) |
Loga (Daemen-Schmid) 7.5 meter cylindrical Made in Switzerland by Daemon-Schmid c1930 |
![]() Loga (Daemen-Schmid) 7.5 meter cylindrical REF |
Daemen-Schmid (Loga) 7.5 meter cylindrical Made in Switzerland by Daemon-Schmid c1930 Archive - Ed Chamberlain Collection |
![]() Loga (Daemen-Schmid) 2.5 meter cylindrical REF |
Daemen-Schmid (Loga) 2.5 meter cylindrical Made in Switzerland by Daemon-Schmid c1930 Archive - Herman's Slide Rule Catalogue ![]() |
![]() Loga Slide Rule REF |
Loga Slide Rule Made in Switzerland - Paper and metal backing Front Scale: Zz(K1), A [ B, R, C ] D, Zz(K2) Back Scale: A [ B, R ] C, Currency Conversions Archive Herman van Herwijnen's Slide Rule Catalogue |
![]() Loga Pocket Slide Rule REF |
Loga Pocket Slide Rule Made in Switzerland - Paper and metal backing Front Scale: K, A [ B, R, C ] D, Log Back Scale: A [ B, R ] C, Currency Conversions Archive Herman van Herwijnen's Slide Rule Catalogue |
Cylindrical Pocket Slide Rule with Helical Scales
Scale effective length 66 in (168 cm) with 4 significant figures.
Otis Carter Formby King biography by Susan Richards
![]() Otis King Classification Types There are 4 principle types, defined by Richard Lyon A, B, C and D and a B/C Hybrid. See Richard Lyon's Website |
![]() Sketch from Colin Barnes article in JOS Vol 4 No 2 |
![]() Patent UK183723 Issued Aug 3, 1922 |
![]() Manual 8 Pages (524Kb PDF) |
Known Scale Sets: 409/410, 414/423, 416/417, 422/424, 429/430
Known Models: K, L, N.
![]() REF Otis King Model K Cylindrical (Type A 1921-1923) |
Otis King Model K Cylindrical (Type A) Made in England - 66 inch scales for multiplication and division Patents: UK 183723 Serial number: Scales: 424 and 422 Archive - Ebay Photo ![]() |
![]() Otis King Model K Cylindrical (Type A 1940) ISRM 14.01.03.03 |
Otis King Model K Cylindrical Made in England - 24mm Dia. x 260mm Long, 66 inch scales Patents: UK 183723 Serial number: 5673 Scales: 423 and 414 ![]() ![]() ![]() ![]() |
![]() Otis King Model K Cylindrical (Type C 1960) ISRM 11.12.29.01 |
Otis King Model K Cylindrical Made in England - 24mm Dia. x 260mm Long, 66 inch scales Patents: UK 183723 Serial number: V7554 Scales: 423 and 414 ![]() ![]() ![]() ![]() |
![]() Otis King Model L Cylindrical (Type B 1960) ISRM 11.12.29.02.X |
Otis King Model L Cylindrical Made in England - 24mm Dia. x 260mm Long, 66 inch scales Patents: UK 183723 Serial number: Z2275 Scales: 429 and 430 Note: Came in Green cardboard box (missing top) ![]() Otis King Type C Model K and L Instructions |
![]() R.H. Smith Cylindrical Slide Rule REF |
R.H. Smith Cylindrical Slide Rule Helical scales Made by J.H. Steward Archive - Conrad Schure Collection |
![]() Barnard's Co-ordinate Spiral Slide Rule ISRM 24.06.10.01 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() Note: the LAT COS (Latitude) and DEP SIN (Departure) scale labels. |
![]() Made in United Kingdom Designed Henry (Henri) Osmand Barnard - (1869-1934). Geodesic engineer. M.S., A.C.H. and Fellow of the Royal Astronomical Society. He was a Superintendent Trigonometrical Surveys, Ceylon (now Sri Lanka) Survey Department. Made by W.F. Stanley & Company See more of his biography in the SR Who's Who page Description from 1914 catalogue: The Co- ordinate Spiral Slide Rule has been designed to meet these requirements by Mr. H. O. Barnard, Like Professor Fuller's rule, upon which it is an improvement, it enables the user to perform Barnard's co-ordinate spiral slide rule.with speed and accuracy arithmetical computations involving multiplication, division, proportion, continuous fractions, powers, roots, and logarithms ; but in addition, the natural and logarithmic values of trigonometrical functions of any angle can be determined by inspection with the same accuracy as in numerical computation, while the products, quotients, etc. , of these functions, by lengths or numbers, integral or fractional, are obtained with equal ease, rapidity and precision . The scope of its operations will be gathered from the examples which are given to illustrate its use in the instructions supplied with the rule. Although the co-ordinate spiral rule, as all varieties of slide rules, is based primarily upon the theory of logarithms, a knowledge of that theory is by no means essential to its practical use.
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![]() Professor Fuller's Calculating Slide Rule ISRM 12.01.03.01.X ![]() ![]() |
Professor Fuller's Calculating Slide Rule Made in United Kingdom by W.F. Stanley & Company - Designed by Prof. George Fuller in 1878. Original owner in UK Description from 1912 catalogue: "Professor Fuller's Calculating Slide Scale, the most accurate od all calculating scales, is equal to a straight slide rule 83 feet long, and gives logarithm, multiplication, division, proportion, etc., results in four or five figures. Its range is greater than that of most arithetical machines, as besides the operationsof multiplication and division which many instruments can only perform, results requiring the reciprocals, powers, roots or logarithms of numbers can be quickly and easily obtained by its use. Largely used by civil, electrical, and mechanical engineers, actuaries, quantity surveyors, etc. In mahagonay case with instructions for use." |
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Wright's Arithmeter No. 8 Cylindrical Slide Rule Made by Joseph W. Fowle, USA, 1869 Materials" Brass and wood. Paper scales on a brass drum. Dimensions of Instrument: 36 cm x 48.2 cm x 48.2 cm; 14 3/16 in x 18 31/32 in x 18 31/32 in Note: Wright sold the Arithmeter to insurance companies for $500.00, though only about 20 were made. ![]() ![]() ![]() Archive - National Museum of American History |
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Wright's Arithmeter No.11 Cylindrical Slide Rule Made by Joseph W. Fowle, USA, 1869 ![]() ![]() ![]() ![]() Archive - Computer History Museum in Mountain View, California |
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