Rarities, Olde and Rare Logarithmic Calculators

Napier's Bones (Rods)

Lord John Napier (latinized Nepero), Baron of Merchiston, Edinburgh, Scotland. Published the logarithm in 1614, after 20 years of developing the tables, which made it possible to perform multiplications and divisions by addition and subtraction and was the foundation for all future slide rule designs. Ex: a*b = 10^(log(a)+log(b)) and a/b = 10^(log(a)-log(b)). He created this calculating tool, which is easy to build out of square dowels.

Gunter's Scale

Gunter's Scale - Two Foot Table of Trigonometry, from the 1728 Cyclopaedia, Volume 2 featuring a Gunter's scale

Gunter's Scale - Two Foot - Circa Early 1800's Made in UK - Made of Boxwood Front Scales: RUM, CHO, SIN, TAN, S*T, SEC, RUM, M*L, CHO, 24 inch and decimal foot, 1/2 inch and 1 inch diagonal scales. Back Scales: S*R, T*R, NUM, SIN, V*S, TAN, MER, E*P. Note: This is the most common Gunter Scale, used for navigation Archive - David M. Riches Collection (UK)

Gunter's Scale - One Foot

Gunter's Scale - One Foot - Circa Early 1800's Made in UK - Made of Boxwood Front Scales: (Left) RUM, CHO, SIN, TAN, S*T, (Center) SEC, (Right) S*R, T*R, NUM, SIN, V*S, TAN, MER, E*P, LEA, RUM, M*L, CHO. Back Scales: 12 inch and decimal foot, 1/2 inch and 1 inch diagonal scales. Note: The upper side has brass pins insert at the scale starts and some gauge points to protect the rule from the divider points at these frequently used places. Archive - David M. Riches Collection (UK)

Sectors

Galileo Galilei (1564-1642) Popularized the sector at the very end of the 16th Century. The sector is a graduated ruler that uses trigonometric formulae and a caliper to calculate squares, cubes, reciprocals and tangents of numbers. Galileo's design of the sector as a mathematical tool can be seen as the moment when calculation aids cease to be based upon counting and instead exploit the deeper relationships among numbers. His invention is still in use as a navigation aid in the 20th century 300 years later.(ref: Oughtred Society) Sectors were frequently included in sets of drawing instruments in the eighteenth and nineteenth centuries until made obsolete by the slide rule. There are three types of scale on an English sector: sectoral ones (radiating from the hinge centre), which were used for calculation; plane scales (logarithms, sines, tangents) parallel to the edge; and rules (inches, tenths of feet). Most were six inches in length. A few images from David M. Riches website. Read this excellent paper on Edmund Gunter and the Sector written by C. J Sangwin, of the University of Birmingham, UK.

ISRM - Ivory Sector (150dpi) Hi-res Image (300dpi) Ivory Sector rotated open Ivory Sector rotated straight to use as 12 inch scale	Ivory Sector Assumed to be made in UK by W&S Jones, No 135 Holburn, London, England Typical nineteenth century sector, having scales for inches, decimal feet, lines of sines, tangents, equal parts, chords, numbers (log scales for multiplication), polygons, secants. Identical to the W&S Jones, David Riches Collection, shown below, but without manufacturer's identical and model markings. Ivory Sector 3 'stars' identification marks
ISRM - Boxwood Sector (150dpi) Hi-res Image (300dpi) Boxwood Sector rotated open Boxwood Sector rotated straight to use as 12 inch scale	Boxwood Sector Assumed to be made in UK. Typical nineteenth century sector, having scales for inches, decimal feet, lines of sines, tangents, equal parts, chords, numbers (log scales for multiplication), polygons, secants. This one, with the protractor was acquired from England. Boxwood Sector single 'star' identification mark Boxwood Protractor used withe Sector in Navigation and calculations
W&S Jones Sector	W&S Jones Sector Made in UK by W&S Jones, No 135 Holburn, London, England Ivory sector. William & Samuel Jones were at this address from 1792 to 1800. This is very typical of nineteenth century sectors, having scales for inches, decimal feet, lines of sines, tangents, equal parts, chords, numbers (log scales for multiplication), polygons, secants. Archive - Image and comments donated by David M. Riches
French Sector	French Sector Made in France. A brass sector dating from the eighteenth century with scales for line of equal parts, polygons, line of chords, metals, weights of shot and gun calibre. Unlike English sectors, which were used for general calculation, the French ones were generally intended for gunnery calculations. Archive - Image and comments donated by David M. Riches
4-1/2 Inch Basswood Sector	4-1/2 Inch Basswood Sector Made in UK dated from the nineteenth century. Sectors were made in various sizes, but most commonly by far in the six inch size. The smaller, 4 1/2 inch ones would have been made to go with small size instruments, probably a pocket set. The scales are the usual English ones. Archive - Image and comments donated by David M. Riches
Elliot Brothers Ivory Sector	Elliot Brothers Ivory Sector Made in UK by Elliott Bros, Strand, London dating from between 1854 and 1880. This is very typical of nineteenth century sectors, having scales for inches, decimal feet, lines of sines, tangents, equal parts, chords, numbers (log scales for multiplication), polygons, secants. It is a six inch size example. Archive - Image donated by David M. Riches

Joint Rules (with Gunter Scales)

The first widely used standard form for a logarithmic slide rule is the two-foot, two-fold design devised by Henry Coggeshall around 1677. This was made in many variants by numerous makers, and is relatively easy to come by even today. Folding joint rules were in common use in the 1800's by capenters and other artisans. The addition of a sliding brass slide with logarithmic, or 'Gunter' scales to one leg of the joint rule added a calculation feature not found on the other similar looking devices. The back of the brass slide was divided into inches which allowed the user to use that part of the rule as a depth gage. When unfolded 180 degrees the rule became 24 inches long, not counting the slide length. Joint rules that are all linear, not having any logarithmic scales, are not included in the ISRM galleries.

ISRM - Carpenters Joint Rule with Gunter's scale on Slide - Unfolded

ISRM - Carpenters Joint Rule with Gunter's scale on Slide - Folded

Carpenters Joint Rule with Gunter's scale on Slide Made of boxwood with brass joint and Gunter's slide, c1890. Front Scale (Top Leg): 12" decimal scale 1/16th increments || A (1-10-100) [ B (1-10-100) C ] D (4-10-40), Girt Line Front Scale (Lower Leg): 1/2:1 Architectural scale. 1/4:1 Architectural Scale, 12" scale 1/16th increments Back Scale (Top Leg):Fractional Measuring Scale 12 - 24 inches. Back Scale (Lower Leg):Fractional Measuring Scale 1 - 12 inches. Back Slide: :Fractional Measuring Scale 1 - 12 inches. Markings: Warranted Best - Box, RD NO 28060, Improved Joint Note 1: the D scale from 4 to 40 is based on the Coggeshall design. Note 2: The Girt line below the slide, is used in calculating the volume of timber ('girt' is a quarter of the circumference of a round log). Note 3: The Gunter's scale is in the format defined by Coggeshall in the 1600's

Issac Aston, Maker

Issac Aston 4-Sided_Box Rule	Issac Aston 4-Sided_Box Rule Made in UK by I. Aston Maker, 25 Old Compton Street, Soho, London c1860 Everard type made of boxwood Side A: ? [ B ] D, on slide: { formula for cask volumes ] Side B: SegST [ C ] SyS Side C: A [ C ] D Side D: Seg Ly [ B ] Sy, on slide: [ ?, Sp D, Variety] Archive - Tom Dilatush Collection
Issac Aston Coggeshall	Issac Aston Coggeshall Carpenter’s slide rule by Isaac Aston, London (working 1851-70), made of boxwood and brass with steel end caps. Isaac Aston (25 Old Compton Street, Soho, London) was succeeded by Aston & Mander. A two foot two-fold rule. Archive - Tom Dilatush Collection

Aston and Mander Makers

Aston And Mander Makers - Carter's Rivet Pitch Calculator	Aston And Mander Makers - Carter's Rivet Pitch Calculator Made in UK, London Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle
Aston And Mander Makers- Dixon Style Slide Rule	Aston And Mander Makers - Dixon Style Slide Rule Made in UK, 25 Compton ST, London Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle
Aston And Mander Makers - C. Hoare Slide Rule	Aston And Mander Makers - C. Hoare Slide Rule Made in UK, 25 Compton ST, London Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle
Aston And Mander Makers - Ship Tonnage Calculator	Aston And Mander Makers - Ship Tonnage Calculator Made in UK, for G.L. Watson Co. Naval Architects and Surveyors 141 Sauchiehall Street, Glasgow Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle
Aston And Mander Makers - 1915 Artillery	Aston And Mander Makers - - 1915 Artillery Made in UK, London Front Scale: Yards [ Minutes of Angle or Battery Range ] Back scale: Yards [ Minutes of Angle ] Archive - Scan donated by Clay Castleberry, California.
Aston And Mander Makers - Timber And Brick Pricing Rule	Aston And Mander Makers - Timber And Brick Pricing Rule Made in UK, 25 Compton ST, London Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle

T.C. Ballardie

T.C. Ballardie - Merchant Vessel Speed And Power Scale

T.C. Ballardie - Merchant Vessel Speed And Power Scale Made in UK, by F. Robson &Co., 46 Dean Street, Newcastle on Tyne Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle

Dring and Fage

ISRM - Dring And Fage - Excise Officers Rule (c1868) Note: This is the oldest physical slide rule at ISRM. It was used for cask gauging with additional rods.	Dring And Fage - Excise Officers Rule Made in UK, Tooley Street, London - Made of Boxwood. 9-1/2" x 2" x 1/4" thick Front Scale: A [ C, C ] SL, 2nd V, 1st V, A [ C, C ] MD (Malt Depth) Back scale: D1 (1-3.2) [ B, B] D2 (3.2-10), H3 V, Y2 V A [ B, B ] SS. SL (Segment Lying), SS (Segment Standing), MD (Malt Depth). Top edge Scale: L (1 in long divisions 0 - 9.5), Sphd (Speroid, Linear 0 - 6.5), Variety (Linear 1 - 6.1) Bottom Edge Scale: log (1-10), log 1.6 - 16). Note 1: Scale. D1 and D2 are the two halves of an 18 inch long log scale Note 2: Gauge marks are identified by brass pins pressed into the wood stock Note 3: MB (Malt Bushel) gauge mark at 2219 denotes a post-1824 rule. Note 4: Embossed with the symbol of Inland Revenue, which occured after 1849 Note 5: It must be earlier than 1880 as it has the malt depth scale and they moved from Tooley street to The Strand in 1883. Note: 6: For another example see Ron Manley's collection. Note: 7: For more information on Gauging see Ron Manley's web page on gauging.
Dring And Fage - Brewers Slide Rule	Dring And Fage - Brewers Slide Rule Made in UK Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle
Dring And Fage - Brewers Slide Rule Set	Dring And Fage - Brewers Proof Slide Rule Set These ivory rules would have come from a Sikes Hydrometer case and are a Proof rule and a Comparative rule. Made in UK Front Scale: TBD Back scale: TBD

F.C. Farmar 10 Glouster Terrace, Thorpe Bay, Essex, England

Farmar's Desk Size Gauging Rule

Farmar's Desk Size Gauging Rule Made in England - Serial Number 8264 Front Scale (Guaging & Stocking): A [ B, C ] D, E, F Back scale (Reducing): G [ H, I ] J, K, KK Edges: Equations and Equivalents Archive - Scan by Peter Fox, UK.

Froude

Froude's Slide Rule Froude's Slide Rule Made in England, Mfg by Stanley Great Turnstile, Holborn, London, England Front Scale: K [ K, C ] D Back scale: A [ B, C ] D Edges: Equations and Equivalents Archive - Scan by Peter Fox, UK.

Fuller

Fuller Rotary Calculator

Fuller Rotary Calculator Made in United Kingdom - Designed by Prof. Fuller Archive

Gravet Lenoir

Gravet Lenoir

Gravet Lenoir - c1900 Made in France - 14 Rue Cassette, Paris Front Scale 25cm // A [ B, B ] D || 25cm Back Scale (Slide): [S, T, L ] Well: 25-52cm Archive - Clay Castleberry Collection

Hannyngton

Hannyngton (Astronomical) Slide_Rule John Caufield Hannyngton (1807-1886) Hannyngton (Astronomical) Slide_Rule Made in England, Mfg by Aston-Mander Size: 32 inchesa x 7.5 inches x 3/4 inch Archive - Scan by Rod Lovette, UK. Designed by Major-General John Caufield Hannyngton and is used in astronomical computations. Fellow of the Institute of Actuaries. His best known and largest work is a Table of Haversines, Natural and Logarithmic, used in computing distances for the Nautical Almanac.

Loftus

Loftus - Brewers Slide Rule

Loftus - Brewers Slide Rule Made in UK, London Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle

C. Mander

C. Mander Sliding Gauge Rule

C. Mander Sliding Gauge Rule Made in UK, London Front Scale: TBD Back scale: TBD Archive - UK Slide Rule Circle

Palmer, Aaron

Fullers Time Telegraph And Palmers Computing Scale

Fullers Time Telegraph And Palmers Computing Scale Made in Boston, United States - Pre 1840 Front Scales: Palmers Computing Scale Back Scales: Fullers Time Telegraph Notes: Made of cardboard, 8-1/2 inch diameter circular scale, on an 11 inch square base. Engraved by George G. Smith, 186 Washington, Boston, Massachusettes. Archive - Scan by Clay Castleberry, California

Palmers Pocket (endless) Scale

Palmers Pocket (endless) Scale Made in Boston, United States - 1845 Front Scales: Palmers Computing Scale Notes: Made of cardboard, 80mm diameter. 143 x 91 mm. Engraved volvelle on heavy card mounted on rear pastedown of book "Palmer's Pocket Scale with Rules for its use in Solving Arithmetical and Geometrical Problems", Rochester, NY. Published by Aaron Palmer, Canfield and Warren Printers, 1845. Engraved by George G. Smith, 186 Washington, Boston, Massachusettes. Archive - Photos by Clay Castleberry, California

John Rabone & Sons

REF Rabone Joint (Carpenter's) Rule

Rabone Joint (Carpenter's) Rule Made by John Rabone & Sons, Birmingham, England. Late 19th century It is a 2 foot, 2 fold example.The scales are few - only the 2-foot linear rule on the back and Coggeshall scales on the front: Three two-cycle logarithmic scales running from 1 to 100 above and on the slide, and a 4 - 40 "Girt line" below the slide, for calculating the volume of timber. Archive - Image donated by Nathan Zeldes

W. Ransley

REF W. Ransley Slide Rule

W. Ransley Slide Rule Made by W. Ransley Maker, Stangate, London, England circa 19th century It is a 2 foot, 3 fold example.The scales are few - only the 2-foot linear rule on the back and Coggeshall scales on the front: Three two-cycle logarithmic scales running from 1 to 100 above and on the slide, and a 4 - 40 "Girt line" below the slide, for calculating the volume of timber. Archive - Image donated by Nathan Zeldes

Roberts

Roberts - Everard Type Gaugers Rule

Roberts - Everard Type Gaugers Rule Made in UK, London - Pre 1824 Scales: Wine and Ale Gallon Marks Notes: The rather nice Roberts, London - Everard type rule has wine and ale gallon marks so is certainly pre 1824 and most likely second half eighteenth century as Roberts would either have been Edward Roberts (1) working 1749-84 or his son Edward Roberts (2) working 1788-96, both at Dove Court, Old Jewry, London. Ref. G C Clifton's Directory of British Scientific Instrument Makers p234. (per David M. Riches) Archive - UK Slide Rule Circle

R.H. Smith

R.H. Smith Cylindrical Slide Rule

R.H. Smith Cylindrical Slide Rule Helical scales Made by J.H. Steward Archive - Conrad Schure Collection

Tavenier - Gravet

Tavenier-Gravet

Tavenier-Gravet - c1900 Made in France- Rue Mayet 19, Paris Front Scale 25cm // A, DF [ CF, CI, C ] D \\ 25cm Back Scale (Slide): [S, L, T ] Cursor: Brass Chisel Point Archive - Rod Lovett Collection

K&E Thacher's Calculating Instrument

K&E 4012 Thacher's Calculating Instrument

K&E 4012 Thacher's Calculating Instrument Made in USA - Designed by Edwin Thacher Archive - Michael O'Leary Collection (USA)

J. Thomlinson Ltd.

Thomlinson's Equivalent Paper Slide Rule (Version 1) Thomlinson's Equivalent Paper Slide Rule Made in UK, J. Thomlinson Ltd. Publishers, Partick, Glasgow Scales: 23in, A(Length) [ B(Breadth), Index ] C(area)[ D(Weight)] E(Standard Bulk Paper sizes L x W), Conversions Archive - Scan donated by Peter Fox, UK

Thomlinson's Equivalent Paper Slide Rule (Version 2) Thomlinson's Equivalent Paper Slide Rule Made in UK, J. Thomlinson Ltd. Publishers, Stanley Works, Partick, N.B. Scales: A(Length) [ B(Breadth), Index ] C(area)[ D(Weight)] E(Standard Bulk Paper sizes L x W) Note: Scales arranged by John Rennie Archive - Scan donated by Peter Fox, UK

Forrest M. Towl

Forrest M. Towl Pipe line Flow Slide Rule Left: Mineral Industry, 1920, Page 472 Right: Handbook of Petroleum Industry, 1922, page 403 Note: This slide rule design and layout was used as the basis for the Dow Chemical Slide Rules made by Pickett, Model 1060.

Forrest M. Towl Pipe line Flow Slide Rule Designed Expressly for the Oil Pipeline industry by Forrest M. Towl, C.E. 1910 Made in U.S.A. Front Scale: Capacity/hr [ AIE, SAE, Dia of Pipe (Inches), Length(Miles), Cd, Sum of Delivery Pressures ] Difference of Delivery Pressures Back scale: [Length of Stroke, Explosions/min, H.P., Ratio of Compression ] Archive - Scan by Rick Mandrell, his father Thomas C. Mandrell (1919-2002) used and collected these slide rules while working for Dow Chemical Co's pipeline department. .

Vade Mecum

Vade Mecum Slide Rule

Vade Mecum Slide Rule Designed Expressly for the timber Trade by George Bousfield, Grimsby. Patent 12806 Made in England Front Scale: 2/16in scale || A [ B, 12-24in, C ] D || 0-12in Back scale: E, F [ G, G, H(OPS)(PTS), I ] J, K Archive - Scan by Clay Castleberry