##
Slide RulesIndex by Purpose

While many slide rules were made as general calculating instruments, for multiplying numbers and solving equations with squares, cubes, trigonometric functions, and logarithms, many others were made to ease the calculations associated with a specific task. Click on items in the list below to see rules in the collection with an identifiable specialized purpose. For comparison, a few illustrative examples of all-purpose slide rules are shown under the link to General Calculation.

"Slide Rules - Index by Purpose" showing 3 items.

## Four-Sided Gauger's Slide Rule by Cook

- Description
- This is a twelve-inch, four-sided boxwood slide rule used in England for measuring and taxing barrels of liquid. Each of the four slides has a brass guide at one end, and the various special points on the rules are marked with inset brass pegs. On one side, the base has a D scale, logarithmically divided from 1 to 3.2 and from 3.2 to 10. Point 18.789 is marked G, the circular gauge point, for determining the mean diameter of a barrel. Point 46.3 is marked MS, for the side of a square vessel that contains a solid bushel per inch of depth, and point 52.32 is marked MR, for the side of a square vessel that contains a malt bushel per inch of depth. The slide has two identical B scales, logarithmically divided from 1 to 10. Point 277.42 is marked G for the imperial gallon.

- On the second side, the base has logarithmic scales that run from 1 to 8 and from 8 to 100. It is labeled SEG
^{T}S^{T}(Segments Standing) at the top left and SS at the bottom right. The slide has two identical C scales, logarithmically divided from 1 to 9. This side was used to estimate the volume of a barrel that was standing vertically and partially filled. The back of the slide lists gauge points, divisors, and factors for circles for malt and for gall (another substance used in making alcoholic beverages) in circular and square containers.

- On the third side, the base has an A scale, logarithmically divided from 1 to 10, and an MD (Malt Depth) scale that runs logarithmically in the opposite direction from somewhat less than 3 to 20. Point 2219 is marked B, for the number of cubic inches in a bushel under the imperial system of measurement, and point 277.42 is marked G, for the imperial gallon. The slide has two identical C scales, logarithmically divided from 1 to 9. The back of the slide has a scale of inches, a scale labeled SPH[EROI]
^{D}, and a scale labeled 2^{D}VAR[IETY]. These scales are for determining the diameters of two different shapes of barrels. Underneath the slide is marked: COOK. MAKER TO THE HON^{BLE}BOARD OF EXCISE. LATE*WELLINGTON*CROWN COURT SOHO*LONDON*N^{O}2950.

- On the fourth side, the base has logarithmic scales that run from 0 to 4 and from 4 to 100. It is labeled SEG
^{T}L^{Y}(Segments Lying) at the top left and SL at the bottom right. The slide has two identical B scales, logarithmically divided from 1 to 9. Underneath the slide, points 3.9 and 99 are connected by a line marked with H.

- The use of the Imperial system of units dates this slide rule to after 1824. It is of the style developed by Thomas Everard in 1683 and, at 12 inches, represents one of the two standard "pocket" sizes (the other was 9"). Laban Cook(e) succeeded Alexander Wellington (d. 1825) as a Maker to the English Board of Excise and remained in business until 1834. Compare to the older rule for gauging and ullage (the amount a container is lacking to be full), MA*319510.

- References: D. Baxandall,
*Catalogue of the Collections in the Science Museum: Mathematics I. Calculating Machines and Instruments*(London, 1926), 42; Colin Barnes, "The Customs and Excise Gauging Slide Rule,"*Journal of the Oughtred Society*4, no. 2 (1995): 53–57; Peter M. Hopp,*Slide Rules: Their History, Models, and Makers*(Mendham, N.J.: Astragal Press, 1999), 72, 245; Gloria Clifton,*Dictionary of British Scientific Instrument Makers*(London: National Maritime Museum, 1995), 64.

- Location
- Currently not on view

- Currently not on view

- date made
- 1825-1834

- maker
- Cook, Laban

- Cook

- ID Number
- 1980.0588.04

- catalog number
- 1980.0588.04

- accession number
- 1980.0588

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Lewis & Briggs Four-Sided Gauger's Slide Rule

- Description
- This is an eight-inch, four-sided boxwood slide rule used for measuring and taxing barrels of liquid. On one end of the rule, the slides on each side have been labeled with the four Roman numerals, I, II, III, and IV. On side I, the base has logarithmic scales that run from 1 to 8 and from 8 to 100. It is labeled Seg S
^{t}(Segments Standing) at the top left and SS at the bottom right. The slide has two identical C scales, logarithmically divided from 1 to 9. This side was used to estimate the volume of a barrel that was standing vertically and partially filled. The back of the slide lists calculating factors used in computing taxes on various liquors. For instance, the duty on one barrel of vinegar was equivalent to the duty on 7.56 barrels of small beer.

- On side II, the base has logarithmic scales that run from 0 to 4 and from 4 to 100. The bottom right corner is labeled SL (Segments Lying) for estimating the volume of a partially filled barrel lying on its side. The slide has two identical B scales, logarithmically divided from 1 to 10. The point 231 is marked W, showing the number of cubic inches in a wine gallon, and pi (314) is marked with a C. The back of the slide has a table of gauge points for converting between volumes in cubic inches and numbers of gallons for substances in square or circular containers.

- On side III, the base has an A scale, logarithmically divided from 1 to 10, and an MD (Malt Depth) scale that runs logarithmically in the opposite direction from somewhat less than 3 to 20. Point 2150 on the A scale is marked MB, for the number of cubic inches in a malt bushel, and point 282 is marked A, for the number of cubic inches in an ale gallon. The slide has two identical B scales, logarithmically divided from 1 to 9. The back of the slide has a scale of inches, a scale labeled Spheroid, and a scale labeled 2
^{d}Variety. These scales are for determining the diameters of two different shapes of barrels. Underneath the slide is marked: LEWIS & BRIGGS : Makers. N^{o}. 52. BOW. LANE. Cheapside. LONDON.

- On side IV, the base has a D scale, logarithmically divided from 1 to 3.2 and from 3.2 to 10. Point 17.15 is marked WG, for the diameter in inches of a cylinder that contains one gallon of wine when filled to a depth of one inch. Point 18.95 is marked AG for the diameter of a cylinder containing one gallon of ale. Point 46.3 is marked MS, for the side of a square vessel that contains a solid bushel per inch of depth, and point 52.32 is marked MR, for the side of a square vessel that contains a malt bushel per inch of depth.

- The slide has two identical C scales, logarithmically divided from 1 to 10. The back of the slide has a table of divisors for converting between volumes in cubic inches and numbers of gallons for substances in square or circular containers. The numbers in this table are squares of the gauge points in the table on the back of the slide on side II. Underneath the slide is marked: Will
^{m}. Wright : April. 30. 1795.

- According to Gloria Clifton, the firm of Lewis & Briggs operated in London from at least 1795 to 1799. The Smithsonian acquired this object in 1961.

- References: Colin Barnes, "The Customs and Excise Gauging Slide Rule,"
*Journal of the Oughtred Society*4, no. 2 (1995): 53–57; Ron Manley, "Gauging," http://www.sliderules.info/a-to-z/gauging.htm; Gloria Clifton,*Directory of British Scientific Instrument Makers*(London: National Maritime Museum, 1995), 167.

- Location
- Currently not on view

- Currently not on view

- Currently not on view

- date made
- 1795

- maker
- Lewis & Briggs

- ID Number
- MA*319510

- catalog number
- 319510

- accession number
- 239015

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## L. Lumley & Co. Gauger's Slide Rule

- Description
- This yew rule has straight brass ends and two slides, which fit between the three parts of the base. On one side, the top scale on the base (labeled A), the two scales on the upper slide (labeled E), the first scale in the middle of the base (labeled D), and the two scales on the second scale (labeled B and C) are identical logarithmic scales that run from 1 to 10 twice in the length of the rule. The second scale in the middle runs from 1 to 100 and is labeled SEG
^{T}S^{T}(segments standing). The lowest scale on the base is labeled SEG^{T}L^{Y}(segments lying).

- These scales are used with the slides to find the volume of the liquid in a cask that is not full, either when it is standing on its base or lying horizontally. The ImB and ImG points, for just over 2200 cubic inches in an imperial bushel and 277.42 cubic inches in an imperial gallon, are marked on the A scale. On the D scale, point 18.95 is marked IG for the diameter of a cylinder containing one imperial gallon; point 46.3 is marked MS, for the side of a square vessel that contains one solid bushel per inch of depth; and point 52.32 is marked MR, for the side of a square vessel that contains one malt bushel per inch of depth.

- The reverse side of the rule has a scale on the base labeled A that runs logarithmically from 1 to 10. Both slides have identical scales (the one on the upper slide is labeled C) that run from over 80 (UNDER PROOF) down to 0 (PROOF) and then up to 70 (OVER PROOF). The middle of the base has a scale labeled B that runs logarithmically from 4 to 40 and a scale labeled C that runs logarithmically from 300 to 30. The bottom of the base has a scale, also labeled C, that runs logarithmically from 100 to 10. There is no indicator.

- One edge of the instrument has a scale labeled SPH
^{D}and a scale labeled 2^{ND}VARIETY. These scales are for determining the diameters of two different shapes of barrels. The other edge is marked: L. LUMLEY & C^{O}L^{TD}1 AMERICA SQUARE LONDON. L. Lumley & Company, a distributor of packing cases and related materials for bottling, was in business in London from at least 1884 though 1929.

- For slide rules with similar two-slide designs but different purposes, see MA*318478 and 1987.0693.01. For earlier gauger's rules, see MA*319510 and 1980.0588.04.

- Reference: Ronald E. Manley, "Gauging," http://www.sliderules.info/a-to-z/gauging.htm.

- Location
- Currently not on view

- date made
- 1884-1929

- maker
- L. Lumley & Company Limited

- ID Number
- MA*320637

- catalog number
- 320637

- accession number
- 242721

- Data Source
- National Museum of American History, Kenneth E. Behring Center