On Napier's work on logarithms:

"The Invention was greedily embraced (and deservedly) by Learned Men." - 1685 by Dr. John Wallis, Savilian Professor of Geometry, University of Oxford. (Ref. 5.)

"The Canon Mirificus is the first British contribution to the mathematical sciences, and next to Newton's Principia it is the most important work in the history of the exact sciences that has been published in Great Britain, at all events until within the memory of living persons.
In whatever country the Canon Mirificus had been produced, it would have occupied the same commanding position, for it announced one of the greatest scientific discoveries ever made."
- 1915 by J. W. L. Glaisher, M.A., Sc.D, F.R.S, Fellow of Trinity College, Cambridge. (Ref. 7) 

 

Introduction: In 1614 John Napier of Scotland published his Mirifici Logarithmorum Canonis Descriptio, a treatise on logarithms together with tables related to the present natural logs. Although not as well known as other groundbreaking books on mathematics / science, it certainly deserves to be so as the use of logarithms was far reaching in e.g. mathematics, astronomy, navigation, finance. It was translated into English by Edward Wright in 1618 and published with the title A Description of the Admirable Tables of Logarithmes (9). The English mathematician Henry Briggs in liaison with Napier constructed tables of logs to the base ten which became the base most widely used. 2014 is the 400th anniversary of Napier's first publication and the Royal Society of Edinburgh has a webpage devoted to 'Napier 400' summarising the events being planned, which include a free exhibition 'Power of Ten: Inventing Logarithms' by National Museums Scotland and some meetings.

Nowadays with calculators or smartphone apps an arms length away providing answers to complex calculations in sub-seconds to umpteen decimal places, its easy to forget how valuable logarithms became when Napier's work was published—as Wallis eloquently summarised in header quote—they were 'greedily embraced'. The potential of logarithms to transform complex multiplication and division to much simpler and less error prone operations using addition and subtraction was quickly recognised, both in tabular form and as logarithmically ruled scales in the form of the Gunter's scale and slide rules. Other workers (8) who are known to have contributed to logarithms and/or exponents include Archimedes (4) and Michael Stifel. Jost Bürgi independently developed his own method for creating logarithmic tables but published later in 1620. Napier's rods (or bones) are a manual calculating device which Napier devised.

As a collector of slide rules and with a casual interest in the history of mathematical tables, this article is my own modest 'raising a glass' to Napier on the 400th anniversary by sharing a gallery of collectables with a wider logarithmic theme—as to date only two have been identified that are directly associated with John Napier. In 2006 Werner Rudowski shared a splendid illustrated article covering the theme of 'Logarithms, Slide Rules and Abaci on Stamps, Coins and Banknotes' (1). I don't wish to overlap his presentation so I concentrate on collectables either published since 2006 or on how known items have been variously presented. I would be interested to learn of other items.


John Napier and other mathematicians:




Above: In 2012 a set of 21 stamps depicting mathematicians in the Deutsche Post 'Marke Individuell' series did feature a portrait of Napier, the only stamp to my knowledge published to date that does. The title page of his 'Descriptio' is also incorporated (left above).
Fortuitously the series also included the German monk and mathematician Michael Stifel whose work is cited by historians in the history of logarithms and exponents. The stamp shows a page from his 'Arithmetica Integra' published in 1544 (see Wikipedia entry).
These 'Marke Individuell' series are end user designs submitted to Deutsche Post for approval but are valid post. The series looks professionally designed and do wonder who instigated them, perhaps an institution in Germany. The individual stamps and full set were previously available on delcampe.net but has been replaced at time of writing by an extensive new set of mathematicians and their work.
Note added Jan. 19th 2014. Thank you to Werner Rudowski who remarks: "One can order a block of 20 stamps, each 60 cents for a total of €39.85, i.e. each one would cost about €2."
Note added October 25th 2015. The above stamps were  designed and issued by Dieter Egelriede who sells them on delcampe.net under his delcampe ID 'Pzbrig2'. With thanks to Dieter for a personal communication.




Nicaragua, 1971, 'Las 10 formulas matematicas que cambiaron la faz de la tierra' ('10 mathematical formulas that changed the face of the earth' - Google Translation).The sea, stars and sextant emphasise the profound impact that logarithms had on navigation / astronomy. Illustrated by Werner Rudowski (1), to date this and the German stamp above, are possibly the only two known devoted to John Napier.
A short biography is presented on the stamp's reverse. A neat idea that could be more widely adopted to describe the theme of a stamp.


Charles Babbage and philately: The majority of logarithmic themed collectables found to date present Charles Babbage and his work. Babbage needs no introduction and is well known for his ambition to build mechanical engines using the method of differences to both calculate and print out error free and accurate tables including logarithms. His difference engine designs were never completed but the Science Museum UK successfully built his Difference Engine No. 2 in time for the bicentennial of his birth on December 26th 2001 (6). The printer was later successfully built and added. Both were shown to work very well. (See below for notes on his Analytical Engine.)


Great Britain, 1991, 'Scientific Achievements'. A stamp showing a profile of a youthful Babbage and a stylised illustration of the method of differences formed part of the Royal Mail 'Scientific Achievements' series. Werner Rudowski illustrated this stamp in ref. 1 remarked on above, but also featured in his fascinating article 'Images of Charles Babbage' discussing and illustrating portraits / photos of Babbage that are known (3). The latter article is useful in identifying which portrait was used where featured in stamp / first day cover designs. Below are additional presented examples of how the Babbage stamp in this series was featured.

Great Britain, 1991, 'Scientific Achievements'. Charles Babbage stamp and the Royal Mail Presentation pack of the series.
 © Stamp Design Royal Mail Group Ltd (1991).

The packs fold out to give illustrated summaries of the themes of the stamps. Left above, shows the design of the biographical entry, right above describes the significance of the equation featured on the pack and some of the first day covers. Three FDC's are shown below but others are known and were issued often on behalf of relevant institutions or societies. © Stamp Design Royal Mail Group Ltd (1991).

Above. Great Britain, 1991, 'Scientific Achievements'. First Day Cover.
© Stamp Design Royal Mail Group Ltd (1991).




Above. Great Britain, 1991, 'Scientific Achievements'. First Day Cover.
© Stamp Design Royal Mail Group Ltd (1991).

Great Britain, 2010, 'The Royal Society 350 Years'. Babbage featured again in a series of GB stamps to celebrate the Royal Society. A photograph of him when older is used with details from an engineering drawing of engine parts.



Above. Great Britain, 2010, 'The Royal Society 350 Years', Charles Babbage stamp and the Royal Mail presentation pack. A short biographical note of each person featured is again included inside the fold out card. © Stamp Design Royal Mail Group Ltd (2010).

Above. Great Britain, 2010, Royal Mail 'Prestige booklet' DX49. For selected Royal Mail thematic stamps since 1980, they have issued a 'Prestige Booklet' which feature both the stamps and more extensive background information on the person and/or theme featured. © Stamp Design Royal Mail Group Ltd (2010).

Above. Great Britain, 2010, Royal Mail 'Prestige booklet' DX49. Showing the stamp pane where Babbage is featured.
© Stamp Design Royal Mail Group Ltd (2010).



Above. Great Britain, 2010, Royal Mail 'Prestige booklet' DX49. Showing the design of the page with a biography of Babbage.
© Stamp Design Royal Mail Group Ltd (2010).

Left above: Republic of Guinea-Bissau, 2007, 'Grandes Inventions'. An attractive stamp with an older portrait of Babbage and engine.

Right above: Gabon Republic, 2001, invention of calculator. A cleverly thought out design incorporating part of a Babbage engine in background and showing the transition from mechanical to thermionic valve to modern integrated circuit calculator designs. Correction Sept. 28th 2018. A discrete transistor is shown not a valve! The progression shown in the design is thus from Babbage's to later mechanical calculators, discrete transistors then to modern calculators which typically use single chip microprocessors for calculation.

Other Babbage themed collectables. The Isle of Man in 1999 issued an attractive FDC featuring a design with Babbage portrait on the envelope and an Isle of Man 1995 one crown coin embedded 'Inventions of the Modern World'. The coin has a stylised design of his analytical engine. This fomed part of the 'Millennium Coin Cover Series'. This is available from a variety of stamp/coin dealers.
Some test currency notes printed by De La Rue also featured intricate designs showing a portrait of Babbage and aspects of his technical drawings. delcampe.net sometimes sell these.

Babbage and trains: I'm not a train buff but while 'Googling' for Babbage related items I stumbled on an attractive detailed working model of a British Rail Class 60 diesel locomotive. Wikipedia informs us that the Class 60 was first in service in 1989 and designed for 'heavy freight' duties such as aggregate, coal and petroleum. The engine numbered 60054 was given the 'Charles Babbage' nameplate. Wiki' notes that examples in this class for coal / petroleum use were named after those who had contributed to science or engineering.

For the collector of all things logarithmic, if ever an excuse was needed to persuade our families that a train set was justified—here's a good reason! Working model locomotives with this detail are quite expensive (typically £70+ on eBay UK), so I'm grateful to a dealer for a photograph of this model.




Product details as stated by Hatton's Model Railways: "Manufacturer [of model]: Graham Farish. Scale: N Gauge. Product Code: 371-354.
Product Title: Class 60 diesel 60054 'Charles Babbage' in BR Railfreight Petroleum sector livery."
Image © Hatton's Model Railways, Liverpool, UK and used with their kind permission.



Wikipedia fortuitously illustrate their Class 60 entry with the real life 'Charles Babbage' engine at high resolution and shared here under the 'GNU Free documentation License' (image cropped and resized) with thanks to the originator 'Janderk1968'

Slide rules and philately: Slide rules and their scales use the principles of logarithms to provide powerful and versatile tools for a range of calculations. The first slide rules were developed only a few years after Napier's publications in 1622 by William Oughtred and others. To my knowledge there are at least ten stamps that show a recognisable slide rule in its design although some examples are admittedly in the 'blink and you'd miss it' category!

Below are all the stamps either previously reported or have come across myself to date that show a slide rule (there are no doubt more), plus a selection of first day covers that feature them on the envelope design. Eking out some examples were a direct result of seeing what photographs depicting a scientist with slide rule had been used on a stamp. The Crick and Watson, Whittle, Fermi and Segrè examples below were found this way with the help of Mike Konshak's splendid gallery of 'Historical Photos of People with Slide Rules and Related Ephemera' on his International Slide Rule Museum website.

A Crick and Watson photo with DNA model: One of the iconic photos that presents Crick and Watson in front of their DNA model shows a slide rule being used as the pointer by Francis Crick. A fascinating and poignant article in the UK Slide Rule Gazette (2) described and illustrated the story behind this series of photographs (and featured on the Gazette's front cover). Some stamps and other philately items have used this photograph as shown below.



Left above: Australia 2003. Maximum card. Collecting maximum cards is a formal branch of philately called maximaphily. They are cards with the stamp placed on the front of a commercial postcard where the subject of the postcard, stamp and postmark show a high degree of concordance. See 'Microscopy themed maximaphily', Micscape February 2013.

Middle above and detail to the right: Great Britain 2009. Cambridge University 800th anniversary, commemorative sheet CS6. The unlabelled stamp attached to the postage stamp showing Crick and Watson is called a 'se-tenant label' and a form regarded to be a legitimate thematic (with thanks to members of the Stamp Community Forum for clarifying its terminology). © Stamp Design Royal Mail Group Ltd (2009).



Above: Togo (République Togolaise) in the 1990s published a series of Millennium sheets celebrating aspects of different decades from the 20th century. This sheet for the 1950s uses the same iconic photo of Crick and Watson (top right of sheet, detail on right).



Left and middle above: Romania, 1957, 'AL2-LEA Congress' depicting a stylised slide rule. These were illustrated by Werner Rudowski in his 2006 article (1).

Right above: German Democratic Republic, 1962, mechanical engineering? A 'blink and you'd miss it example' but believe a slide rule is shown.



Republic of the Congo, 1964, University Lovanium 20th anniversary. The far left stamp forms part of an adhesive sheet of unperforated stamps, the middle and right are discrete perforated stamps. Again the slide rule barely features but collectors of such a very narrow theme can't be too fussy!



Russia 2012, Marina M Raskova, female pilot and navigator, celebrating 100 yrs since her birth. See Wikipedia entry for a biography. An attractive design with sufficient detail for knowledgeable collectors to recognise as a real slide rule model and thought to be 'an early NL-type' (with thanks to Ronald van Riet, see discussion on Yahoo International Slide Rule group ).



USA First day cover 2001. This is again based on a photograph of Fermi and both the photograph and this FDC are shown in the International Slide Rule Museum gallery. The back of the envelope states the image source: 'Original painting for the First Day Cover by Gherman Komlev. Authorised by Ms. Rachel Fermi.' © Fleetwood.

Comments to the author David Walker are welcomed.

Acknowledgments:
Thank you to the Director of Hatton's Model Railways for permission to use the model train image.
Thank you to Werner Rudowski for his article in reference 1 which inspired me to start my own collection and to seek other examples since it was published. Also for his useful suggestion for the article.
Thank you to Mike Konshak for his International Slide Rule Museum website. The site's extensive photographic gallery showing scientists using slide rules provided leads to seek out a number of stamps showing slide rules.
A number of the free access links in the references below above to specialist literature are hosted on Rod Lovett's website where he meticulously maintains a large database of specialist literature in collaboration with the appropriate journal / magazine publishers.

Images of Royal Mail stamps and related material used under their guidelines on this not-for-profit educational website.

Note on image use: The copyright of all images where not specified if not known, remains with the originator(s). Both these and those where the owner is not specified have been used under the US 'Fair Use' of copyrighted material guidelines for use in an educational and not-for-profit review context as Micscape is hosted in the USA. Image size is modest to allow only screen use. Images showing extensive text are at a size / crop to show the design elements only. 'Right clicking' to save an image offline has also been disabled.

Note added February 22nd 2015. Since writing this article, the server has moved from the USA to the UK. 'Citing the US 'Fair Use' policy for third party image use (widely used e.g. by Wikipedia) is thus no longer valid. The article has been retained as an educational resource on this not-for-profit website. If a copyright holder objects, please contact the author above and we will be pleased to remove the image or change/add any image credit. Thank you.

Note on sourcing items: My favourite source of thematic stamps and other collectibles is delcampe.net where the prices are often cheaper than eBay or dealers with their own websites.

Notes on descriptions: I have not included stamp catalogue numbers (e.g. Stanley Gibbons, Michel, Scott) as I'm interested in the topics depicted on stamps rather than the associated philately and don't have access to the catalogues. Most dealers specialising in thematics offer searches on a given theme.

References
1) Werner H Rudowski, 'Logarithms, Slide Rules and Abaci on Stamps, Coins and Banknotes', UK Slide Rule Circle 'Gazette', 2006, August, Issue 7, pp. 61-65. (Available to read on Rod Lovett's website.)
2) Colin Barnes and Rod Lovett, 'The Making of an Iconic Image', UK Slide Rule Circle 'Gazette', 2012, August, Issue 13, pp. 1-6.
3) Werner H Rudowski, 'Images of Charles Babbage', UK Slide Rule Circle 'Gazette', 2006, August, Issue 7, pp. 7-14. (Available to read on Rod Lovett's website.)
4) Peter Holland, 'Archimedes - His Approach Towards Logarithms', Journal of the Oughtred Society, 2005, Volume 14, No. 2, pp. 17-21. (Available to read on Rod Lovett's website.)
5) John Wallis, 'Treatise of Algebra', Chapter 12, page 55 'Of Logarithms and their Use', 1685 and chapter reprinted in 'Sherwin's Tables', 1705/6 and later editions. (Link is to a hi-res facsimile on the 'ECHO Cultural Heritage Online' website.)
6) Doron Swade, 'The Cogwheel brain', 2000, Abacus Little Brown and Company.
7) JWL Glaisher in 'Logarithms and Computation, Napier Tercentenary Memorial Volume, Ed. C G Knott, Longmans, 1915. (Link is to www.archive.org copy.)
8) Florian Cajori, 'Algebra in Napier's day and alleged prior inventions of logarithms', ibid, pp.93-109.
9) Edward Wright, 'A Description of the Admirable Table of Logarithmes', 1616 and later editions. (Available in modern fascimile copies from bookshops. The Renascent Books (UK) edition is excellent, 2013. Available from Amazon UK in paperback.)
10. Ioanne Nepero [John Napier], 'Mirifici Logarithmorum Canonis Descriptio', 1620. (The Google Books link is to the 1620 edition with additional contributions by Henry Briggs.).


Additional selection of resources (Not linked to in the text.)
- Logarithms: The Early History of a Familiar Function by K M Clark and C Montelle, in the 'Convergence' Series published by the Mathematical Association of America. A superb and very accessible set of illustrated articles online presenting clear explanations of logarithms and their development by Napier and Bürgi, which was very different from our modern concept of logarithms.
- William Rae Macdonald', 'The construction of the wonderful canon of logarithms. Translated from Latin into English with notes and a catalogue of the various editions of Napier's works', William Blackwood and Sons, 1889. (Link is to www.archive.org copy. The original Latin 'Construction' was written before the 'Description' but published after John Napier's death by his son Robert in 1619.)
- Robin J Wilson, 'Stamping Through Mathematics', Springer, 2001, 126pp. A delightful extensively illustrated book.
- Lynne Gladstone-Millar, 'John Napier. Logarithm John', National Museums Scotland, 'reformatted and reprinted' 2013, 64pp. Copiously illustrated in colour and black and white, a very accessible and rounded history of his life, his work on logarithms and their impact to this day. Excellent value at <£5 new from Amazon UK Marketplace.
- Werner H Rudowski, 'Images of John Napier, Baron of Merchiston', UK Slide Rule Circle 'Gazette', 2005, August, Issue 6, pp. 77-85 and later update in 2006. (Available to read on Rod Lovett's website and ... An Update in Issue 7, 2006, pp.45-46.)


Related 'Micscape Lite' articles
'A selection of portable calculating aid designs spanning over 2000 years', Micscape August 2013.
'The Appeal of Slide Rules - For Use and as Collectables', Micscape December 2012.
'Some typical slide rules under the low power microscope', Micscape December 2013. (PDF file)

First published January 13th 2014, revised January 19th, 2014.
Revised October 20th 2015, corrected date of Stifel's 'Arithmetica Integra' to 1544.
Revised October 25th 2015. German stamps showing Napier and Stifel credit added as now known to be Dieter Egelriede.
Revised September 28th 2018, corrected caption to the Gabon Republic 2001 stamp.

 

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