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Otis King's Pocket Calculator

Otis King's Pocket Calculator Model K

Otis King's Pocket Calculator, Model K
Articles and Advertisements

Otis King's Pocket Calculator, Model K

Otis King's Pocket Calculator is compact cylindrical variation on the slide rule. At the base is a cylindrical handle with a logarithmic scale that spirals around it. There is an opaque tubular sleeve around this with a marker that you can set to any point on the scale. Out of the other side of this marker tube is another cylinder, again with a logarithmic scale, which can be moved independently, and also be set to align with another marker on the sleeve.

On the outer end of the handle it says Made in Britain, with the serial number T8866. This dates this one to about 1962.

Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K

It came in a small cardboard box with an instruction leaflet.

Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K

Otis King's Patent Calculator     (PDF, 1.99 MB or archive.org)
Carbic Limited
8-page folded leaflet
127mm × 203mm

This instruction leaflet explains multiplication, division, proportions and percentages, and for the model L also logarithms, powers and roots.

Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King's Pocket Calculator Model K
Otis King Calculator Instructions
Otis King Calculator Instructions



Otis Carter Formby King patented his design for a cylindrical slide rule in 1921 (see GB 183,723). At that time he worked for A. King and Co., a grocers company based in Stoke, England, which may have been a family business. Note however that just a few years earlier he was working for the English Electric Company in London (see GB 137,972, a patent for a clutch). I imagine that he was between jobs and fell back on the family business to tide him over. The address on these early calculators was apparently 44 Bray's lane, which matches King's address in his 1921 patent, and A. King and Co. was also located on the same street.

From 1923 the calculator was made by Carbic Ltd., 51 Holborn Viaduct, London. In King's 1923 patent (GB 207,856) he gave this as his address. Carbic was a company that had been located at this address for some time even before King designed his calculator. It is unclear how or why Carbic came to be involved in the manufacture, and I have been unable to verify whether Carbic also made the calculator in 1921 or 1922.

Carbic Limited was floated as a new public company in 1910, with Charles Cheers Wakefield as its director. Sir Charles Wakefield had already made his fortune in oil and lubricants, having founded the Castrol company, and his services to the City of London earned him his knighthood. He was the Lord Mayor of London in 1915-1916, and his further philanthropic deeds evantually led to him becoming a baron and then a viscount.

Carbic Limited were specialised in carbide lamps and oxy-acetylene welding. Carbide, or calcium carbide, reacts with water to produce the highly flammable acetylene. Carbide degrades by reacting with the moisture in the air, and it is tricky to regulate the reaction with water. The company had been founded to exploit their patented invention of carbic cakes, sealed tablets of carbide which don't degrade and are much easier and safer to handle (see US 975,306). They produced these carbic cakes, as well as lamps and portable welding equipment that made use of them. Otis King joined the company, presumably around 1923. He designed an oxy-acetylene blowtorch for them in 1926 (GB 251,091).

Otis King left Carbic to work for A. Reyrolle & Company in around 1927 (see GB 307,379), and seems to have had no further involvement with the calculator that bears his name. Carbic continued to produce the Otis King Calculator until the early 1970s.


There were 13 different models, indicated with the letters A to N (skipping the letter I). They mostly differ by the two scales that are used. In some models the lower scale is slightly larger, making the handle shorter and the marker tube longer. By far the most common models are the K and L, because those are for general calculations, while the other models are specialised for money, weights, or time calculations.

Model K has two logarithmic scales - the bottom scale covers one order of magnitude (i.e. 1 to 10) while the top scale is twice that length, covering two orders of magnitude (i.e. 1 to 100). This allows for easy multiplication and division. On the model L the double-length top scale is replaced by one logarithmic and one linear scale so that exponentiation, roots, and logs are also possible.

There were two main types of scales for currency: The Retail Cash scale that ranged from 1 penny to 100 pounds, and the Wholesale Cash scale that ranged from 1 shilling to 1000 pounds. Similarly there was a Retail Weights scale (1 ounce to 156 pounds) and a Wholesale Weights scale (1 quarter to 28 tons).

A:Retail Cash, vulgar fractions
B:Retail Cash, decimals
C:Wholesale Cash, vulgar fractions
D:Wholesale Cash, decimals
E:Retail Cash, Retail Weights
F:Retail Cash, Wholesale Weights
G:Wholesale Cash, Retail Weights
H:Wholesale Cash, Wholesale Weights
J:Wages Cash (1 penny to 8 pounds), Time
K:Long logarithmic scale
L:Logarithmic scale, linear scale
M:Metric scales
N:Cash (1/4 penny to 1000 pounds), vulgar fractions, weights

Articles and Advertisements

Here are some articles and advertisements about Carbic Limited, but unrelated to the calculator.

1909-11-02 Westminster Gazette
1910-06-09 Westminster Gazette
1910-10-20 Daily Mirror
1910-10-20 Western Daily Press
1911-02-04 The Economist
1911-05-26 Engineering
1911-11-24 The Engineer
1911-12-30 Country Life
1912-01-27 Railway Times
1912-10-18 The Engineer
1912-11-02 Country Life
1913-03-29 The Spectator
1914 Debretts baronetage knightage and companionage
1915-07-15 Shipbuilding and Shipping Record
1915-11-04 Shipbuilding and Shipping Record
1917-04-05 Flight
1918-06-27 Engineering News-Record
1919-04-10 Liverpool Journal of Commerce
1922-06-29 The Foundry Trade Journal
1922-07-13 The Foundry Trade Journal
1925-02-05 Liverpool Journal of Commerce
1922-06 The Welding Engineer

Here are some articles and advertisements of the Otis King calculator.

1921-10-20 Coventry Evening Telegraph
1921-10-29 Kenilworth Advertiser
1922-02-27 Coventry Evening Telegraph
1923-02-22 The Foundry Trade Journal
1923-06-29 The Builder
1923-06-29 The Electrical Review
1923-10 The Mathematical Gazette
1923-10 Mechanical Engineering
1924-01-11 Engineering
1924-06-19 The Board of Trade Journal
1924-12-27 Nature
1925-06-26 Engineering
1925-08 Scientific American
1925-09 Popular Science
1926-01 Scientific American
1926-07-29 Coal Age
1926-08-07 Nature
1928 Surveying drawing and nautical instruments
1930-01-25 Nature
1939-12-23 Nature
1950-07 Chambers's Journal
1956-09 Design
1957-09-21 Science News Letter
1959-03-04 McGill Daily
1960-06 Personnel Management & Methods
1960-10 Personnel Management & Methods
1961-11 Personnel Management & Methods
1968-03 Compressed Air
1970-10 The Chemist
1971-04-05 The Economist
1971-05 Administrative Management
1972-04 Journal of Advertising Research
1972-05 Reprographics & Engineering Records Management
1972-06 The Chemist
1972-11 Everyday Electronics
1973-07-12 New Scientist


Below is the list of patents related to the Otis King Pocket Calculator. Otis King has a few other patents to his name, which are assigned to whoever was his employer at the time. These include a clutch (GB 137,972 for the English Electric Company), a blowtorch (GB 251,091 for Carbic Limited), and electric remote control (GB 307,379, GB 307,381, GB 307,383, GB 307,384, GB 307,385, and GB 310,984 for A. Reyrolle & Company).

PatentFiling datePublish dateNameDescription
GB 183,72320-08-192103-08-1922Otis Carter Formby KingCalculating Apparatus
GB 207,76204-09-192204-12-1923Otis Carter Formby KingExtra cylinders, extra scales, extra marks
See also: CA 241,986, DE 418,814, FR 569,985.
GB 207,85604-09-192204-12-1923Otis Carter Formby KingDesktop version
See also: CA 241,076, DE 418,669, FR 576,616, US 1,645,009.


Otis King's Patent Calculator by Dick Lyon has a lot of information.
Rechner Lexikon has a page on the Otis King with a list of models.
Cris Vande Velde has rare old model M and model N calculators.
The Oughtred Society has an article by Peter Hopp with a table of serial numbers and one by Bob Wolfson with a look Inside the Otis King Calculator.
Vintage Calculators Web Museum has a model L.
Wikipedia has articles on Otis King and Charles Wakefield.
Grace's Guide has entries on Carbic, Charles Wakefield, and Otis King.
Sir Harry Bhadeshia shows a model L with a brief explanation and a scan of the instruction leaflet.
Bob's Calculators and Slide Rules shows a model K and model L and has disassembly instructions.
Original Documents on the History of Calculators by Andries de Man has web versions of the Otis King instruction leaflets.

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