From Pascal to Burroughs: what did mechanical calculating machines give the accountant?

We have a separate article about the abacus. This time we look at another family: calculating machines with gear wheels. Their history reveals an interesting pattern: behind almost every new machine stood a specific problem of a tax collector, an insurer or an accountant.

For whom did Pascal build his machine?

According to MacTutor (University of St Andrews), in 1639 the Pascal family moved to the city of Rouen, because the father, Étienne Pascal, had been appointed tax collector for Upper Normandy. Britannica writes that the young Blaise Pascal invented a calculating machine in 1642–1644 to make his father's work easier. It later came to be called the Pascaline.

The Computer History Museum adds several important clarifications:

Pascal was not the first: the German scholar Wilhelm Schickard built a calculating machine around 1623;
Pascal built about 50 machines but sold only about 15;
the Pascaline performed only addition and subtraction.

Leibniz taught the machine to multiply

According to Britannica, the German scholar Gottfried Leibniz designed his machine in 1671 and built it in 1673. It performed multiplication by repeated addition and shifting of digits. The Computer History Museum writes that the stepped drum devised by Leibniz (a cylinder with teeth of different lengths) influenced the design of calculating machines for about the next two centuries.

The insurer's arithmometer

According to the Smithsonian, the Frenchman Thomas de Colmar received a patent for a calculating machine in 1820, and it too was based on stepped drums. The London Science Museum Group notes that Thomas was the founder and director of two insurance companies in Paris. The Smithsonian writes that the British insurance company Prudential Assurance was one of the important early customers of the arithmometer. The insurer and the accountant: the machine's first serious buyers.

Keys and paper tape: Felt and Burroughs

At the end of the 19th century machines began to work with keys instead of a turning crank:

The comptometer. According to the Computer History Museum, the American Dorr Felt received a patent for the comptometer on 11 October 1887: simply pressing a key added the number.
The Burroughs machine. William Burroughs received a patent for a calculating machine on 21 August 1888. The museum writes that within a year he built about 50 machines, but they were difficult to use; the inventor then improved them.
Printing. The "Registering Accountant" in the Smithsonian collection is one of Burroughs' early printing, full-keyboard machines. It was made by the American Arithmometer Company of St. Louis; the company was later renamed the Burroughs Adding Machine Company.

For an accountant, printing matters a great deal. An ordinary machine shows only the result, while a machine that prints on tape leaves every number entered on paper. If there is an error, you can compare the tape line by line with the documents and find which number was keyed in wrongly. This is the mechanical ancestor of today's requirement that "every entry should leave a trace".

The electronic calculator

According to the Computer History Museum, in 1961 the British company Bell Punch introduced the ANITA calculator; it is generally recognised as the first commercial all-electronic desktop calculator. Interestingly, it ran not on transistors but on vacuum tubes. We wrote about the next stage, the pocket calculator and the computer, in the article about the abacus.

Then and now

Aspect	The era of mechanical machines	Today
Types of operation	Only addition and subtraction on the Pascaline; multiplication after Leibniz	Any formula, function, analysis
Entering a number	Turning a wheel, turning a crank, later keys	Keyboard, scanner, automatically from an electronic document
Trace of the result	Paper tape only on printing machines	The software keeps every entry, its author and its time
Who used them	Tax collectors, insurers, office accountants	Every accountant, and every person via their phone
Finding an error	Comparing the tape with documents by hand	The software shows the difference itself, the auditor opens the trail

Example: tape and formula

At the end of the month Gulnora, the accountant of the "Chorsu Mato" shop, checks the total of 60 receipt documents (compiled by the author, hypothetical figures). According to the documents the total should be 48 350 000 soum, but the calculation came out at 48 530 000. The difference is 180 000 soum.

Method	How it finds the error	Approximate time
Non-printing calculator	Re-keys everything; the result may differ again	30–40 minutes
Calculating machine with tape	Compares the tape with the documents line by line	10–15 minutes
Spreadsheet or accounting software	Each document is a separate row; the wrong row is seen at once	2–3 minutes

A simple arithmetic rule helps here: if two digits of a number are transposed when keyed in, the resulting difference is always divisible by 9 without remainder. 180 000 ÷ 9 = 20 000, and indeed, 1 350 000 soum in one document had been keyed in as 1 530 000. Without a tape or a spreadsheet, finding such a line would mean re-keying everything.

Conclusion

Calculating machines sped up accounting, but the biggest gift to accounting came from the printing machine: leaving a trace of every number. Today's accounting software has extended this idea even further: it records when, by whom and on the basis of which document each entry was made.