One Turn Too Many

The third advantage in Willgodt Odhner’s 1890 sales booklet was infallible operation. The seventh was a low price. Between them came elegant appearance, easy handling and freedom from oiling. He had made a mechanical calculator small enough to occupy a modest corner of a desk, and hoped it would eventually find a place in every large business.

Later in the same booklet, he explained what to do when the user turned the handle once too often.

The remedy was simple: make a complete turn in the opposite direction. That would undo the unwanted turn. But complete meant complete. A partial revolution could introduce another kind of error. The promise of accurate calculation came with a small, precise set of movements, which the booklet taught through sums, multiplication, division and interest on a loan.

Odhner was a Swedish engineer working in St. Petersburg, the Russian imperial capital. His arithmometer belonged to a developing family of calculators with adjustable teeth inside their wheels. It could retain a number, add it repeatedly and subtract it again, saving the user from writing out every intermediate sum. Two separate displays kept track of different things. Understanding those displays was as necessary as learning to turn the handle.

Teeth to match a number

An ordinary gear has a fixed number of teeth. The calculating wheel in Odhner’s 1878 American patent had nine that could slide out from its rim or withdraw into it. Beside the wheel was a setting disc with a shaped groove. Moving its lever made the groove push a chosen number of teeth outwards. A setting of three exposed three teeth; zero left none projecting.

When the crank carried that wheel round, its exposed teeth engaged another gear connected to a numbered wheel. Three teeth moved the number wheel three places. The wheels alongside handled tens, hundreds and higher places; a separate carrying mechanism passed a completed ten into the next column. One revolution could therefore transfer a whole number into the result register.

The number could stay set while the machine added it again.

That made multiplication a matter of repeated turns. The carriage carrying the number wheels could also slide sideways. Moving it one position changed which decimal columns met the calculating wheels: a turn could now add ten times the set number. A second shift made it a hundred times as much.

The production machine of 1890 incorporated substantial revisions. Its instructions had the user read the settings from the curved cover, move the carriage between fixed stops and return the handle to its starting position before shifting. Wing nuts cleared the two registers independently. The larger windows showed the accumulated result; the smaller ones recorded the turns, with their value determined by the carriage position.

Six turns instead of twenty-four

The booklet’s second example was 49,563 multiplied by 24. With both registers cleared, the operator set 49,563 on the cover. Twenty-four positive turns would add that number twenty-four times. The movable carriage offered a shorter route.

Four turns first produced 198,252. Then the operator shifted the carriage one place for tens and made two more turns. Each now contributed 495,630. The result was 1,189,512, while the smaller display read 24. Only six revolutions had been necessary.

The smaller register read 24 rather than six because its columns recorded four units and two tens. The operator had chosen the multiplication, set the number, supplied the turns and moved the carriage at the right moment.

The next example, 87,659 multiplied by 6,034, used the same principle on a larger scale. Four turns handled the units, three handled the tens, then the carriage moved two places to pass over the zero hundreds column. Six final turns supplied the thousands. The two displays finished at 528,934,406 and 6,034.

Reversing the crank subtracted. Division was repeated subtraction, with the small register collecting the quotient. For 8,450 divided by 26, the booklet instructed the user to subtract at the appropriate positions three times, then twice, then five times. The quotient was 325 and the remainder zero. If an extra turn took the subtraction too far, the user made one turn back before continuing.

The first machine did not undo everything

That correction had once been less satisfactory. In his account of the early machine, historian Timo Leipälä reproduces the criticisms made by engineer Viktor Kirpichev in 1878. A reverse turn restored the numerical result, but left the revolution counter two turns away from the correct reading. Multiplication and division depended on that counter. Correcting one display could therefore spoil the other.

The review concerned the small batch made at Ludvig Nobel’s St. Petersburg factory in 1877. Starting the crank could require the operator to hold the machine down with the other hand, especially with every digit set to nine. Kirpichev saw a simpler, more compact alternative to the established Thomas arithmometer, with practical defects still to remedy.

Yet some of those early machines found durable employment. Government actuaries, who made calculations for public finances, used them in the United States. One belonged to Ezekiel Brown Elliott; after his death, his assistant Mrs S. Wollard bought it. Another belonged to Treasury actuary Joseph S. McCoy. The Smithsonian’s surviving McCoy machine bears the number nine on several internal parts and retains the maker’s name alongside Nobel’s.

The handle was only part of the work of making a calculator useful.

Nobel declined to continue financing the enterprise. Odhner found another backer to pursue patents, then took a job in 1878 at the imperial establishment that made banknotes and state papers. A workshop of his own followed in the 1880s; the revised calculator reached the market in 1890. Its manufacture shared premises and skills with other precision work, including printing machinery.

The improved design also travelled under a different name. In 1892, Grimme, Natalis & Co. acquired production rights for Germany, Belgium and Switzerland and called its calculator Brunsviga. The first Brunsviga instructions reused Odhner’s eight examples and added a ninth. A user learning the new name could still be working through familiar arithmetic.

A closer look · 6:40 · English captions

Turns, shifts and the wheels beneath

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What the numbers were for

The 1890 booklet ended by taking its reader beyond abstract multiplication. What interest was due on 35,876 roubles for 43 days at five per cent? The calculation used a 360-day commercial year. The operator multiplied, cleared the turn counter, set the divisor and divided; the answer rounded to 214.26 roubles. Deciding the interest convention and placing the decimal point remained outside the mechanism.

There was also a useful way to make a conversion table. Set the number of Russian pounds in a kilogram, then turn repeatedly to obtain the equivalents for two, three and four kilograms. Odhner claimed that the figures would appear faster than they could be written down. His calculator produced numbers in windows, leaving their transcription to a person with a pencil.

At Mälaremejeriet, a dairy near Stockholm, an early production machine remained useful long after the first sales booklet. When the business bought a new Odhner in 1911, the old calculator, numbered 50, passed to the sales agent. It was exhibited that September at a Stockholm business show.