#
Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

"Science & Mathematics - Overview" showing 2082 items.

Page 165 of 209

## Dutch El

- Description
- This layered, curved wooden rule has a twisted handle with an ivory crown at the end. A piece of whalebone (2.4 X 1.5 cm) is carved with two horizontal lines and an "X" and is fastened to the rule just below the handle. The measuring part of the rule is 52 cm (20-1/2") long, considerably shorter than the average Dutch el (68–72 cm), a traditional "arm's length" measure used before The Netherlands adopted the metric system in 1820. Also unlike Dutch els such as MA*318246, MA*318247, and MA*325404, there are no grooves marking off distances. Instead, horizontal rows of three nails are placed 5, 9.2, 17.8, and 35 cm from the base of the handle. A diagonal row of four nails is adjacent to the last horizontal row. One layer of wood has been removed from the tip of the rule.

- Location
- Currently not on view

- date made
- before 1820

- ID Number
- MA*318248

- accession number
- 235392

- catalog number
- 318248

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

## Pocket Case of Drawing Instruments Signed Martel

- Description
- This miniature sharkskin pocket case is lined with green cardboard. An emblem of cherries is imprinted on the top and bottom of the case. The case holds 3-1/4" silver and steel fixed-point dividers; a hollow silver scribe with a pen point that inserts into the tube and a pencil lead inside the tube; and a 3-5/8" silver French-style sector. (See http://americanhistory.si.edu/collections/object-groups/sectors.)

- One side of the sector has double scales of chords, running from 10 to 90, and for inscribed regular polygons, from 12 sides to 3 sides. A scale for diameters of bullets, running from 1/4 to 30, is along the outer edge of both legs. This side is marked: MARTEL (/) A GENEVE.

- The other side has double scales of equal parts, running from 10 to 100, and for the specific weights of six metals. The outer edge of both legs has a scale for the caliber of shot, running from 1/4 to 27. A scalloped piece fits between the arms of the sector and may be used to lock the instrument into position. A square piece inside the hinge has a pinhole for a plumb line, although no plumb line is present.

- Pierre Martel (1706–1767) was a Swiss engineer, mathematics teacher, maker of mathematical instruments, and geographer who used his own instruments to observe and explore glaciers in the Alps in 1742. He worked in Geneva from 1723 to 1743, in London from 1743 to 1746, and in Jamaica from 1746 to 1761.

- References: Peter H. Hansen,
*The Summits of Modern Man: Mountineering After the Enlightenment*(Cambridge: Harvard University Press, 2013), 32–33; Adler Planetarium,*Webster Signature Database*, http://historydb.adlerplanetarium.org/signatures/.

- Location
- Currently not on view

- Currently not on view

- date made
- 1723-1743

- maker
- Martel, Pierre

- ID Number
- MA*318453

- accession number
- 235072

- catalog number
- 318453

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

## Complete Mathematical Chart Designed by C. W. Goodchild

- Description
- This object consists of paper laminated to both sides of two wooden boards that are held together by two brass hinges and fastened with a brass hook. The front gives instructions for using the 100-line logarithmic table that appears on the inside two pages. To multiply, the user looked up the first multiplicand, noted the number of the line on which the multiplicand appeared, and measured the distance from the left of the line to the multiplicand. Then, the user repeated the process with the second multiplicand. The product appeared on the sum of the line numbers at the sum of the distances. (For instance, the number 4 is on line 60 and the number 2 is on line 30, so the number 8 is on line 90.)

- The table could also be used for division, calculations of interest, finding logarithms, and finding the numbers when the logarithm is known. A diagonal scale at the bottom of page three allowed for interpolation of values. A card or ruler was necessary for recording the distances. The back of the object has a 31-line chart of trigonometrical ratios for finding logarithmic sines and cosines. The bottom of the back is marked: Copyrighted September, 1893, by C. W. GOODCHILD.

- Cecil Wray Goodchild (1847–1900) was born in England but lived in central California by 1880. By 1893, he was a civil engineer and attorney in San Luis Obispo. He designed this chart to meet the needs of those surveyors, engineers, and accountants who required greater accuracy in their work than that provided by an ordinary slide rule, but who did not wish to purchase an expensive instrument such as the Thacher cylindrical slide rule.

- In 1903 and 1906, Keuffel & Esser advertised his invention as the Goodchild Mathematical Chart, model 4019. It sold on paper for 75¢ and on a flat board for $2.75. For an additional $5.00, K&E offered a sliding triangular rule for recording and adding the line numbers and distances.

- References: Library of Congress,
*Catalogue of Title-Entries of Books and Other Articles Entered . . . Under the Copyright Law*, no. 116 (18–23 September 1893): 19; "A Slide Rule Fifty Feet Long,"*The Cornell Daily Sun*14, no. 83 (31 January 1894);*Catalogue and Price List of Keuffel & Esser Co.*, 31st ed. (New York, 1903), 298;*Catalogue and Price List of Keuffel & Esser Co.*, 32nd ed. (New York, 1906), 317.

- Location
- Currently not on view

- date made
- 1893–1903

- inventor
- Goodchild, C. W.

- ID Number
- MA*318472

- catalog number
- 318472

- accession number
- 235479

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

## Tavernier-Gravet Mannheim Simplex Slide Rule

- Description
- This fourteen-inch boxwood Mannheim linear slide rule has a brass indicator in the single chisel style with an open interior. There are no endpieces. The top edge is beveled and has a scale of 35 centimeters, divided to millimeters. The top of the base has a scale divided logarithmically from 1 to 10 twice, and the bottom of the base has a scale divided logarithmically from 1 to 10. These are the usual A and D scales, although they are not lettered.

- One side of the slide has the same two scales (the usual B and C scales, although they are not lettered). The other side of the slide has a scale of tangents that runs from 0 to 45 degrees and is lettered T; a scale of equal parts that runs from 0 to 1,000; and a scale of sines that runs from 80 to 0 and is lettered S. Compare to MA*318474. A paper table glued to the back gives geometric formulae, physical constants for the latitude of Paris, units of measure in France and in England, rates of exchange for common currencies, specific gravities, expansion coefficients of various gases, temperatures of melting and boiling for various solids and liquids, and similar data.

- The bottom of the base is marked: TAVERNIER – GRAVET; RUE MAET 19.PARIS. The back is marked: MÉDAILLES D'OR 1878 ET 1889. Keuffel & Esser donated this rule to the Smithsonian. As with MA*318473, K&E imported it to sell while the company developed the ability to manufacture its own slide rules. Also like MA*318473, the scales and indicator resemble the ten-inch model 479–2 (subsequently numbered 1746N and 1746), but a rule of this length (scales about 14" long) is not listed in K&E catalogs. The ten-inch version with brass indicator cost $4.50 between 1883 and 1890. In 1892, the single-chisel indicator was replaced with a double-chisel indicator.

- References: Florian Cajori,
*A History of the Logarithmic Slide Rule and Allied Instruments*(New York: Engineering News Publishing Company, 1909), 55–58, 80–81; Francis Wells and Tom Wyman, "La Règle à Calcul: Lenoir, Gravet-Lenoir, and Tavernier-Gravet Slide Rules,"*Journal of the Oughtred Society*11, no. 1 (2002): 23–27; Bob Otnes, "Keuffel & Esser — 1880 to 1899,"*Journal of the Oughtred Society*10, no. 1 (2001): 18–28;*Catalogue of Keuffel & Esser*, 17th ed. (New York, 1883), 93;*Catalogue of Keuffel & Esser*, 20th ed. (New York, 1887), 129;*Catalogue of Keuffel & Esser*, (New York, 1890), 131.

- Location
- Currently not on view

- date made
- 1889-1892

- maker
- Tavernier-Gravet

- ID Number
- MA*318474

- catalog number
- 318474

- accession number
- 235479

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

## Keuffel & Esser 4090-3 Log Log Trig Duplex Slide Rule

- Description
- This ten-inch mahogany duplex slide rule is coated all around with white celluloid and held together with L-shaped metal end pieces. The front of the base has LL0, A, T, S2, and S1 scales, with B, K, and CI scales on the slide. The LL0 scale is a log log scale of decimal quantities. The A and B scales are identical, divided logarithmically from 1 to 10 twice in the length of the scale in the usual manner. The K scale is also divided logarithmically, but three times in the length of the scale, for use in finding cubes and cube roots. The CI scale is divided logarithmically from 1 to 10 the length of the scale, going in the opposite direction from the A and K scales. The T scale is a scale of tangents and cotangents, doubly numbered with angles given in degrees and minutes. The S1 and S2 scales are scales of sines and cosines, doubly numbered. The top of the base is marked in red: KEUFFEL & ESSER CO.N.Y.; PAT. APRIL 1.'24 OTHER PAT. PENDING; MADE IN U.S.A. The left end of the slide and the front of the rule are marked with a serial number: 448333.

- The back of the base has L, LL1, DF, D, LL3, and LL2 scales, with CF, CIF, and C scales on the slide. The right end of the slide is marked in red: < 4090-3 >. A glass indicator has white plastic edges held together with metal screws. One edge is marked: KEUFFEL & ESSER CO.N.Y. The other is marked: PATENTED AUG.17.15. (/) OTHER PAT. PENDING.

- Keuffel & Esser advertised model 4090-3 from 1933 to 1936. However, the combination of scales on this example was only issued in 1933, when the rule sold for $10.00. The serial number is consistent with this date. In 1937, model 4090-3 was replaced by model 4080-3.

- References: Adolf W. Keuffel, "Log Log Duplex Slide Rule" (U.S. Patent 1,488,686 issued April 1, 1924);
*K&E Slide Rules and Calculating Instruments*(New York, 1933), 10–11;*Catalogue of Keuffel & Esser Co.*, 38th ed. (New York, 1936), 316–317; Dieter von Jezierski,*Slide Rules: A Journey Through Three Centuries*, trans. Rodger Shepherd (Mendham, N.J.: Astragal Press, 2000), 71–75; Clark McCoy, ed., "Collection of Pages from K&E Catalogs for the 4090-3 & 4091-3 Family of Slide Rules," http://www.mccoys-kecatalogs.com/KEModels/ke4091-3family.htm.

- Location
- Currently not on view

- date made
- 1933

- maker
- Keuffel & Esser Co.

- ID Number
- MA*318479

- accession number
- 235479

- catalog number
- 318479

- 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

## Straight Edge Signed I. R. C. Co.

- Description
- This undivided black hard-rubber rule is beveled along both long edges. It is marked: I. R. C. CO. (/) GOODYEAR. Scratched on the back of the rule is: Brereton. IRC, or Inoue Rubber Company, was established in Japan in 1926 to make bicycle tires and tubes. The reference to Goodyear is likely to the manufacturing process pioneered by Charles Goodyear and not to the Goodyear Tire & Rubber Company. Brereton was presumably the original owner of the instrument, which was acquired by the Museum in 1961. Compare to MA*327306.

- Reference: IRC Tire, "About Us," http://www.irc-tire.com/en/bc/company/

- Location
- Currently not on view

- date made
- 1926–1961

- ID Number
- MA*319738

- accession number
- 239019

- catalog number
- 319738

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

## Flemish Ell

- Description
- This square, tapering wooden rule has a brass tip around the narrow end. Three sides are finely carved with fruit and vines, possibly oranges and pineapples. The fourth side is marked with inlaid brass dots: ANNO IIV DB 1757 NAVW. Inlaid brass bars provide measuring marks that are 1, 3.8, 6, 10.2, 18.7, 26, and 53 cm from the wide end. The spacing of the marks is similar to those on MA*318246. The overall length of the rule is 70 cm (27-1/2"), which is close to the usual length for a Flemish ell (68.6 cm, 27").

- Reference: Herbert Arthur Klein,
*The Science of Measurement: A Historical Survey*(New York: Simon & Schuster, 1974), 57.

- Location
- Currently not on view

- date made
- ca 1757

- ID Number
- MA*319778

- accession number
- 239771

- catalog number
- 319778

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

## Dring & Fage Timetable Sliding Rule

- Description
- This yew wood and brass rule finds the number of weeks between two dates that were up to two years apart. The months of the year are listed along the right edge, from January to December, twice. The month names are adjacent to a continuous calendar for the 24 months, with seven days per row. A brass slide to the left of the calendar is numbered from 1 to 104 (for two years of weeks). A ring at the top for hanging the rule is marked: TIME TABLE. Dock companies used the rule to compute storage charges for goods shipped to or from British ports.

- The right edge is marked: DRING & FAGE MAKERS TOOLEY S
^{T}LONDON. The English firm established by John Dring and William Fage operated at various locations on Tooley Street from 1792 to 1882. For another timetable, or rent, rule by this maker, see inventory number 1954–305 at the Science Museum in South Kensington, London, http://www.sciencemuseum.org.uk/objects/mathematics/1954-305.aspx. The Science Museum owns several dozen other objects by this maker; see http://collectionsonline.nmsi.ac.uk/detail.php?type=related&kv=2628&t=people.

- The back of the rule is stenciled: HWE. The Smithsonian acquired this object in 1962. No further information on the original owner is available.

- Reference: Adler Planetarium,
*Webster Signature Database*, http://historydb.adlerplanetarium.org/signatures/.

- Location
- Currently not on view

- date made
- 1792–1882

- maker
- Dring & Fage

- ID Number
- MA*320636

- catalog number
- 320636

- accession number
- 242721

- 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