Slide Rule Wristwatches



Corrections, comments and additions to Art Simon

What is a slide rule watch?

The Slide Rule Wristwatch has been described as the pinnacle of pre-ic high tech. It's the ultimate analog gadget--not only does it tell the time, it's also a calculator. You might use a slide rule watch to do currency converstions while traveling, calculate the cost of meal with tip at a restaurant, or if you are a pilot planning a flight plan, even more technical calculations like fuel burn, wind correction, and time en route.

A slide rule wristwatch has two logarithmic scales. Usually, one scale is on a movable bezel, and a second is fixed or printed on the face of the watch. Calcuations are made by rotating the bezel to fix the relative position the two scales. The two scales form proportions that are useful in math problems involving multiplcation and division. For example, here's how I might calculate the cost of a meal in a restaurant after including the tip. For a 20% tip, I could line up 12 on the outer ring above 10 on the inner ring. Now all the numbers on the outer ring are 20% higher than the numbers on the inner ring. If my check was $15, the total cost of the meal with tip will be the number on the outer scale above 15, which is $18. If the check was for $150, I could find that the cost with tip was $180, just by ignoring the zeros.

Let's say I was traveling in Europe and wanted to convert euros to dollars. Since 1 euro will buy around 1.4 dollars (ouch!) I could line up 14 on the outer scale with 10 on the inner dial. Now all the numbers are in proportion with the outer scale representing dollars and the inner dial representing euros. To find out how little $10 is worth, I could look at the number on the inner scale under 10. To find what 5 euros is worth, I'd look at the number on the outer scale that is above 5. (For more instructions on the use of a slide rule watch see Casio's Watch with slide rule FAQ)

The slide rule is sometimes confused with a tachymeter, a single scale on some wristwatches that is used with the second hand to calculate speed.

The origins of the Slide Rule Wristwatch

The first slide rule watch was probably this pocket watch designed by Meyrat & Perdrizet in France near the turn of the century. Rechnerlexikon, a German website on mechanical computing describes it in an article on the history of slide rules as "a French pocket watch, with a slide rule around the clock dial, was probably the first real watch with a slide rule." It gives the date of the watch as 1890. Much of the early history of slide rule pocket watches is obscure, and it's not helped by the fact that the term "Pocket Watch Slide Rule" is often used for a slide rule in a pocket watch case that has no time keeping ability. (Photo from Edwin Datschefski's slide rule watch site)

The slide rule wristwatch has a relatively recent origin, arriving in 1940 during the beginnings of World War 2. The beginning of war brought an influx of orders to the Swiss watch manufacturers from all over the world, and with it came the introduction of new watch models with new features. There is some dispute about who manufactured the first slide rule wristwatch, but it was certainly a Swiss firm. The first three slide rule wristwatches came from Breitling, Juvenia and MIMO (Manufacture Internationale de Montres Or). It appears that the extremely rare Mimo-Loga may have been first, with its patent application appearing on July 27, 1940, just weeks before Breitling's patent for the Chronomat was submitted on August 26, 1940. The Juvenia Arithmo doesn't seem to have become commercially available until later, around 1945. (The French page Le Breitling Chronomat et les premières montres avec règle à calcul does an excellent job researching the patents for the early slide rule watches.) (Mimo-Loga scan from Peter from Germany & Juvenia Arithmo photo from Edwin Datschefski's slide rule watch site)

These first three slide rule wristwatches each used a different set of scales for the slide rule. The only reason I can see for this is that there were concerns of violating each other's patents. The Mimo-Loga used the C and D single-decade logarithmic scales from the standard slide rule. These scales are are useful for multiplication and division, and the numbers on both scales increase from left to right. By contrast, the early Breitling Chronomats used the C and CI "inverted" scales, which are useful for calculations involving reciprocals but can be used for multiplication and division as well. These inverted scales can be seen in Breitling's 1940 Swiss government patent application for a circular slide rule mounted on a wristwatch. The submitted drawing shows a slide rule with an an inner scale running left to right, but the numbers on the outer scale running right to left. The Juvenia Arithmo used a third arrangement with three logarithmic scales: C, D and CI. The Arithmo's C and D scales are layed out in reverse running right to left. The innermost scale is the CI "inverted" logarithmic scale, running left to right. The Arithmo also has a magnifying glass ring on outside of the bezel ring to aid in reading the scales

In 1952, Breitling introduced a new slide rule wristwatch with a significant innovation. The first three slide rule wristwatchs were designed with scientitists, engineers, and mathematicians in mind. However Breitling's new model, called the Navitimer, was intended for pilots. This model has defined what is known as the flight computer watch. The Navitimer has the same two C and D log scales as the Mimo-Loga, running left to right, but probably avoided infringing on the Mimo-Loga patent by adding a third scale from the pilots circular slide rule (also known as the E6B "whiz wheel") for time and distance calculations. In addition, the Navitimer was marked for kilometers, statute miles and nautical miles at locations that allow quick conversions from one unit to another. Later flight computer watches have added markings for additional unit conversions (e.g. gallons, liters, pounds, kilograms, etc.) but are otherwise functionally identical to the first Navitimer. The name was a combination of the words Navigation & Timer, since the watch allowed pilots to make calculations useful to navigation as well as to tell the time. It was adopted by the AOPA (Aircraft Owners & Pilots Association) as their official watch, and the early Breitling Navitimers have the AOPA wing logo prominantly displayed on the dial.

Modern Slide Rule Watches

Except for a Mimo-Loga variation that was briefly released by Girard-Perregaux, a brand which was owned by parent company MIMO, no other watch manufacturers introduced any slide rule models until the 60s. Swiss patents have a term of 20 years, and so it's probably no coincidence that after the Mimo-Loga patent would have expired other slide rule watches began to appear using its layout. In fact, the scale layout used by the Mimo-Loga has since become the standard for virtually all slide rule watches. With the exception of some models in the Breitling for Bentley line, all current slide rule watches use the same scale layout as the Mimo-Loga, with the two C and D scales running left to right. The other scales from the standard slide rule which are used for roots, trigonometry, logarithms or other mathematical operations are not used on wristwatches. (Slide rules are generally not useful for addition or subtraction.)

These new slide rule models of the 60s and early 70s came first from Swiss brands like Gallet, Selectron, Agon, Ollech & Wajs, Eberjax, Cimier and later from Sinn, Mondia, Heuer, Fortis and many others. The Japanese introduced models as well with Seiko introducing it's first slide rule watch in 1969 and Citizen producing a model in the early 70s. By the nineties, even the mass market budget brand Casio had introduced slide rule models, and now many inexpensive Chinese watches with slide rules have also become available.

Modern slide rule watches can be broadly categorized between those that use only two scales, like the Mimo-Loga and flight computers that incorporate a third time-distance scale like the Breitling Navitimer. A very small number of slide rule watches (like the Camy Rally King and Citizen RecordMaster Rally Custom) have only one logarithmic scale that rotates around a fixed time scale. This layout would be useful only for making time-distance calculations (presumably of interest to rally divers) and not generalized multiplication and division problems. There are also watches that have only one logarithmic scale presumably for decoration since a single scale wouldn't be of any use in making calculations.

While there are only a few variations of the slide rule used on watches, there are many variations of the watch. They can have an analog, digital or combination display, and have a mechanical, self-winding or battery-operated quartz movement. Most incorporate a stopwatch (called a chronograph movement), and can also include a day, date or moonphase display.

Problems with Slide Rule Watch Accuracy

Unfortunately, not all slide rule watches feature accurate slide rules. While the logarithmic scales were well understood over a hundred years ago, sloppy manufacturing means that many modern slide rule watches don't have the correct spacing of the "tick" marks on the scales. This throws off calculations, in extreme cases by nearly 10%. To check a slide rule watch for accuracy, turn the outer scale until all the numbers coincide with the inner scale, then check to see that all the tick marks are aligned around the two scales. The picture at the very top of this page shows a Ventura Vmatic-Loga with very good accuracy--all the numbers line up correctly. The following picture of the "Tufina Black Mamba" shows what appears to be some inaccuracy. Notice that "50" marks line up correctly, but at the the other side of the dial, the "25" marks are off by two tick marks. Multiplying 10 by 25 on this watch would give a result of 260!

A Survey of Slide Rule Watches

What follows is a survey of some of the manufactures of slide rule watches and some of the different models that have been produced. While slide rule watches are a very small fraction of the entire wristwatch market, it would be a daunting task to compile a comprehensive inventory of all the manufacturers and the models they have produced.

Breitling

Breitling has pretty much defined the slide rule watch, and any survey of the manufacturers of slide rule watches should start with Breitling. Since World War 2, Breitling has produced a long line of slide rule watches, briefly interrupted only by the financial difficulties that plagued all Swiss watchmakers when the quartz watch became popular in the late 1970s. The Chronomat was produced with a slide rule from it's introduction until 1978. This page from the Breitling 2001 catalog has some of the first Chronomats.

Breitling introduced an automatic chronograph in 1969. This is page 26 of Chronosports 1969 catalog showing one of the first automatic Chronomats (white face) along with one of the first automatic Navitimers (black face). Interestingly, the automatic Chronomat doesn't use the inverted scales of the manual Chronomats, but has the now standard C and D scales both running left to right. The automatic Chronomat model also differs with an added tachymeter scale marked in UPH (units per hour) like some Omega and Rolex models. (Scan from OnTheDash.com The definitive online guide to Heuer chronographs and dashboard timepieces)

In 1978 financial difficulties forced Breitling to stop all watch production. The company was sold in 1979. After the change in ownership, new Breitling models began to appear in 1980. The Chronomat eventually reappeared in the Brietling line-up in 1984, but it was a completely different watch without a slide rule. Breitling's current range does include the Chrono-matic, a watch styled similarly to the automatic Chronomats from the seventies.

Breitling has had at least one Navitimer in its line up since its introduction in 1952. There have been many different versions, and it is probably fair to say that the Navitimer is the cornerstone of the Breitling brand. The Navitimer is the watch that distuiguishes Breitling from its competitors. Here's a nice page from the Breitling 2003 catalog that shows some historic Navitimers. The rarely seen LCD model is just visible at the top right.

Not all Navitimers have the third time-distance scale. I've always like the clean appearence of the Navitimer Montbrillant, but only recently noticed that it lacks a time-distance scale. Here's some from the 2001 Breitling catalog:

After the Navitimer, the next big innovation came in 1961 with the introduction of the Cosmonaute, a 24hr version of the Navitimer. It was an idea suggested by Scott Carpenter, one the astronauts in the Mercury program. He asked Breitling if they would make a 24-hour version of the Navitimer pilot's watch, something which would be more appropriate for an astronaut. He was one of the first astronauts to wear a wristwatch in space, wearing his aboard the Aurora 7 spacecraft in 1962. Ironically, given it's origins with the American space program this watch eventually becomes known as the Cosmonaute! (Scott Carpenter photo from http://www.expeditionexchange.com/omega/indexmain.shtml)

Jeff Stein shared this photo of his early Cosmonaute. It's probably the same month of production as Scott Carpenter's.

Robert from Germany shared this photo of his 809 Cosmonaute from 1965.

Here's a nice Cosmonaute Chrono-matic from the seventies. (Photo from http://www.cetec-info.org/JLMichel/Breitling.jlm.html)

Here are some Cosmonautes from the 2007 line.

For the most part, Chrono-matics, Navitimers and Cosmonautes are styled much the same as they were decades ago, so to the modern eye they can have a sort of retro appearence. Breitling continues to introduce new slide rule watches with more modern styling. Here's a good example--the automatic B2 from the 2003 Breitling Catalog.

None of the modern styles have had the longevity of the Navitimer, and some are dropped shortly after their introduction, such as the unloved and rarely seen Navitimer LED model with slide rule. (Photo from Edwin Datschefski's slide rule watch site)

After Breitling reemerged from bankruptcy it continued to produce mechanical, automatic, and quartz models with slide rules. My favorite quartz model is the cleanly styled Jupiter Pilot. Here's a couple pages from Breitling's 1994 catalog, which was one of the last years this model was produced.

Here are a couple of Breilting's Digital-Analog hybrids; the Chronospace, from the 1994 catalog and the AirWolf from the 2007 line. Note that the Chronospace on the left has the optional mini UTC watch that can be fitted into the band.

Breitling also has a Breitling for Bentley line that has some of the only watches I'm aware of that use the C and CI inverted slide rule scales. The inner scale runs left to right, but the outer scale is inverted running right to left, just like the early Breitling manual-wind Chronomats.


Page 2: Ollech & Wajs, Sinn, Hacher and Heuer slide rule watches

Page 3: Other Swiss slide rule watches

Page 4: Japanese slide rule watches--Seiko, Citizen, Casio, Orient and Kentex

Page 5: Other slide rule watches


References


Most of the information and many of the pictures on this page came from other websites.
The official Breitling website
Le Breitling Chronomat et les premières montres avec règle à calcul
Breitling Chronomat a short history Part 1
Breitling Chronomat a short history Part 2
E6B Flight Computer "whiz wheel" Wikipedia article
Slide Rule Wikipedia article
Breitling Navitimer - a breif history
MATH WATCHES - Protractor and Slide Ruler Timepieces
Breitling Navitimer - by Kurt Broendum
Breitling Cosmonaute - the history and development of a legend
Chuck Maddox's page on the Heuer/TAG-Heuer Pilot's Model Chronographs
Breitling and analog-digital
Heuer watch company history
REVIEW: Citizen "Navihawk" or How I Learned To Tell the Time in 30 Cities Around the World
Watches: The Pilots Watch
Tachymetre dial on Omega watches
Ollech & Wajs, Aviation chronographs and the Breitling heritage.....
Sinn 903 review
On the Dash: The definitive guide to Heuer Chronographs
History of slide rules (German)
Many thanks to Edwin Datschefski whose website inspired me and who kindly shared so many photos of slide rule watches.
And many thanks to S. Ford for his patient interest, suggestions and great watch finds!