Adding and Calculating Machines
Stepped-Drum, Pinwheel, and Direct Multiplication
Stepped-drum and pinwheel calculating machines were advertised principally for use
in multiplication and division, particularly multiplication of large numbers and
other complex calculations. Numbers were entered by moving slides or levers.
This method of entering data was slower than with a keyboard, and the machines
could not compete with adding-listing machines and key-driven calculators for
applications requiring high volumes of addition and subtraction. To speed up
data entry, eventually keyboards were added to stepped-drum calculators. Michael
R. Williams states that "All these machines were better suited to
scientific calculations requiring many operations on a few numbers than they
were to the problem of adding up long lists of numbers often found in business
applications. The labor of setting up a number on the machine, by moving a slide
on the Arithmometer type of [stepped-drum] machine or setting a lever on the
Brunsviga [pinwheel] type, was slow enough that it made the devices impractical
for many commercial firms. Although various models existed that used some form
of depressible keys as the input mechanism, these were generally not reliable
enough for high-speed operation." ("Early Calculation," in W.
Aspray, ed., Computing Before Computers, 1990, p. 53.)
(1921, p. 135) wrote that stepped-drum calculators, which were made
by a number of non-U.S. manufacturers, were "used to a considerable extent in Europe
and to a limited extent in the United States." E. H. Beach, Tools of
Business, 1905, states that "The Tate's Arithmometer is in use of
actuaries and mathematicians in all parts of the world." In 1905, the
12 figure model sold for $300 and the 16 figure model sold for $350. A 1914 ad for the TIM and
Unitas calculating machines stated, "The constituent companies of the
American Tobacco Company are using two hundred fifty of our machines. The
constituent companies of the U.S. Steel Corporation are using four hundred of
our machines." The Office Appliance
Manual (1926, p. 56) stated that stepped-drum calculators had been sold
"under names such as Tim, Saxonia, Peerless, Tate, Archimedes, and so
forth." Judging from serial numbers, few if any brands of stepped-drum calculators sold more than 10,000
Undersides of Delton and TIM Stepped-Drum Calculating Machines
Pinwheel calculators were invented in the mid-1870s by both Frank S.
Baldwin in the US and W. T. Odhner in Russia. "The operation of machines of
this type was accomplished by means of pulling levers or knobs in order to set
up the desired number. Addition, subtraction, multiplication, and division were
accomplished by means of revolving drums. For addition they revolved in one
direction, and for subtraction the direction was reversed. For multiplication
the revolutions were repeated in the same direction as for addition, and for
division they were repeated in the same direction as for subtraction. Two sets
of dials provided a means of reading totals. In one the accumulation of totals
appeared; in the other, there appeared the figure which was added, subtracted,
multiplied, or divided." (The Office Appliance Manual, 1926, p. 88)
In the US, sales of pinwheel calculators were small compared to sales of adding-listing
machines and key-driven calculators. Pinwheel calculators were much more popular in Germany than in the US. Brunsviga began production of pinwheel
calculating machines in 1892, and in 1913 it offered 20 different models.
In 1913 Brunsviga stated that in total it had sold more than 20,000 machines
worldwide; in 1915 it stated that the total was over 26,000. US sales of Brunsviga machines would have
been considerably smaller. In 1915, California-based Marchant stated that most of its sales during
1911-15 were on the West Coast. Its list of users included 99 city and county
clerks, assessors, auditors, treasurers, and street departments, 41 engineering
and surveying bureaus and companies, 28 railroad and traction companies, 13
insurance companies, 106 companies in a wide range of other industries, and
three universities. New pinwheel calculators were still advertised in
Germany in 1960.
Both stepped-drum and pinwheel calculators performed multiplication by
successive addition and division by successive subtraction. "For
example, if it be given to find the product of 756.48 by 98.7, it would be
necessary to add successively 7 times, 8 times, and 9 times the number 756.48,
which represents a total of 24 operations." Few early calculators performed
direct multiplication, which involves "adding the multiples of digits
directly to the accumulator numeral wheels instead of pumping it into the
accumulator wheels by repeated addition of the digits" (Turck 1921, p. 181).
Leon Bollée's calculating machine was an early example of a direct
multiplication calculator. This machine could find the solution of 98.7 times
756.48 in three operations. [Add illustration from Office
was the first marketed calculating machine that performed direct multiplication.
It was advertised as "The Fastest Multiplying or Dividing Machine in the
World." Worldwide sales of the Millionaire, which was
sold from 1895 to 1935, apparently amounted to only 4,700 units.
In 1906, a Millionaire was $400 and Thompson stated: "This machine is
especially adapted for use in railways, insurance companies and large
manufacturing plants, and for all cases where percentages or unit costs are
required to very great accuracy." (E. W. Thompson, Book-keeping by
Machinery, New York, 1906, p. 85) Around 1907-08, W. A. Morschhauser, the sole US agent, published a list of US
clients that were using a total of just under 300 Millionaires. Metropolitan Life Insurance Co. had 15, Prudential Insurance Co. 15,
and 48 other insurance companies had a total of 63. The Cleveland, Cincinnati,
Chicago & St. Louis Railway had 14, Baltimore & Ohio Railroad Co. 9, and
43 other railroads and traction companies had a total of 54. Eighty companies in
a wide range of other industries had a total of 95. The Department of Commerce
had 4, the University of Michigan had 3, and 19 other government bureaus and
universities had a total of 20. A 1914 ad stated that 55 big railroad systems
used Millionaires. As of 1921, only one other calculating machine with direct multiplication
had been marketed, the Moon-Hopkins
As one measure of comparative popularity of different types of machines in early
US offices, we have seen a great many office photographs with Burroughs Adding
Machines, and a good number with Comptometers. We have seen only one office photograph that included a
pinwheel calculator and none that included a stepped-drum or direct
multiplication calculator. Presumably the explanation for this is that
pinwheel, stepped-drum, and direct multiplication calculators were used largely
in scientific and engineering applications, rather than in routine office work.
Referring to pinwheel and Millionaire machines, in 1906 Thompson
stated: "there are some expensive machines now on the market which perform
multiplication and division very expeditiously; and they are now in limited use
by some concerns having large amounts of such work." He also stated
that pinwheel calculators were not quite as rapid as Millionaires for
multiplication and division. At that time, a pinwheel calculator with 8 columns
was $250 and a Millionaire was $400. (Thompson, 1906, p. 19)
In addition to several of the machines listed in the following
table, Archimedes, Layton's Improved Arithmometer, and Mercedes-Euklid stepped-drum calculating machines were exhibited in Edinburgh,
Scotland, in 1914. (James W. Cortada, Before the Computer, 1993, Table
Click to Enlarge
Johann Cristoph Shuster
Courtesy of Christie's
Grant's Calculating Machines
In 1871, at the age of 22, George Barnard Grant (1849-1917) of Massachusetts
published "On a New Difference Engine," American Journal of
Science and Arts (Aug. 1871). In this article he described his
invention of a calculating machine based on the method of
differences. Between 1872 and 1898, Grant patented and manufactured desk top calculating machines. He received
the following patents:
|US Patent No.
||July 16, 1872
||Dec. 30, 1872
||Apr. 29, 1873
||Modifications to the
specifications of the preceding patent.
||June 24, 1878
||Aug. 16, 1887
||Awarded more than
nine years after the application.
||Feb. 20, 1895
||June 7, 1898
In 1876, Grant exhibited a calculating machine at the Centennial
Exhibition in Philadelphia. He is reported to have invented this
machine while a student at the Lawrence Scientific School at Harvard
University. This machine was reported to be "intended for use
in counting houses, insurance offices, etc.," and was described as
"a smaller instrument for common operations in multiplication,
division, etc. It is a foot in length by half as much in height and
width, weighs twenty pounds, and contains less than 400 pieces, less than
75 of which are working parts. It takes numbers up to nine decimal
places." (Spencer F. Baird, ed., Annual Record of Science and
Industry for 1876, Harper & Brothers, New York, 1876, pp. 43-44)
According to an exhibition report, this "machine, or arithmometer,
successfully rivals the well-known one of Colmar." ("General
Report of the Judges of Group XXV," in United States Centennial
Commission, International Exhibition, 1876, Philadelphia,
1877) See also Appletons' Cyclopaedia of Applied Mechanics, 1878.
In 1881, Grant exhibited a calculating machine in his home state and won a
gold medal. The report of the exhibition stated: "This
calculating machine has now stood the test of practical use, several of
the machines having been employed during the past three years. It is
admirably adapted for an extensive range of computations in multiplication
and division, and surpasses all other instruments now used for such
computations in respect to simplicity, strength, compactness, durability,
cheapness, rapidity and accuracy of operation." (Fourteenth
Exhibition of the Massachusetts Charitable Mechanic Association,
Boston, 1881, p. 202)
In 1883, an advertisement identified "George B. Grant....Maplewood,
MA, manufacturer of Grant's Calculating Machine." (J. J. R.
Croes, Statistical Tables from the History & Statistics of American
Water Works, New York, 1883)
In 1894, Manufacturer and Builder (Sept. 26, 1894, pp. 195-96)
carried an illustrated article about Grant's calculating machine.
A machine of this type is in the Smithsonian
Institution's National Museum of American History, Washington, DC. A
photograph of this type of machine is posted on IBM's
web site, which reports that it was manufactured by the Grant
Calculating Machine Company of Lexington, Mass., and was an improvement on
the original Grant machine.
In 1898, Encyclopaedia Britannica reported that there were numerous
crank operated calculating machines for multiplication and division,
including machines made by Thomas, Tate, Odhner, Baldwin, and Grant.
"Grant's machine consisted of a cylinder bearing a set of rings on
which were the numerals. These he terms adding-rings. A similar set
of rings is placed on a shaft below, and these he terms registering
wheels. In order to multiply, the adding-rings are set to read the
multiplicand, and the registering-wheels the multiplier. If the
multiplicand were 387,432, the crank would be turned three times and a
slide shifted, then eight times and a slide shifted, and so on. At
the conclusion of the turning the answer could be read on the
recording-wheels." (New American Supplement, Encyclopaedia
Britannica, Vol. II, 1898, p. 651)
In 1901, a book aimed at engineers stated that "Several very
excellent machines for multiplying and dividing are now made. Of these we
may mention, as moderate in price and of perfect accuracy, the calculating
machine of George B. Grant of Boston; the Brunsvega...and the Comptometer.
... The Grant machine, developed from 1874 to 1896, has now reached a high
degree of perfection, and its price is within the reach of any engineering
laboratory." (Rolla C. Carpenter, Experimental Engineering,
5th ed., New York, 1901)
Pinwheel Calculating Machines
|Baldwin Calculating Engine
Frank S. Baldwin
Courtesy of the Museum of Business
History and Technology
National Museum of American History, Smithsonian
Institution, Washington, DC.
Made in U.S.
The Spectator Co., New York, NY (US sales agent)
1905 Price $250
|Brunsviga Multiplying and
(a.k.a. Brunsviga Reckoning or Calculating Machine)
Odhner Patent 1874 ~ Other Patents 1906-10 ~ Production Began 1892 ~
Advertised in US 1907-25
Grimme, Natalis & Co. AG
1915 Prices $175-$400
1924 Prices $275-$425
Advertised in US 1908-24
Newer model advertised in Germany 1960
Triumphator Works, Ltd.
1916 Price $250
1924 Price $250-$350
|Thales Multiplying and
Advertised in US 1914
Rastatt, Baden, Germany
1914 Price $225-$250
On market 1916
Culmer Engineering Co.
New York, NY
|No image available
Standard Pony Marchant Calculating Machine
Patented 1911-15 ~ Introduced 1911 ~ Advertised 1915-25
Electric machine (with outboard motor) introduced 1915
Marchant Bros., Oakland, CA
Marchant Calculating Machine Co., Oakland, CA (1915)
1915-17 Price $250 (13-digit) & $300 (18-digit)
1917 Price $360 Electric Model 4007
1924 Price $350 Model X-L
Machine labeled Marchant Bros.
Stepped-Drum and Other Calculating
Invented 1820 ~ Improved and sold during the remainder of the 19th century
National Museum of American History, Smithsonian
Institution, Washington, DC
Probably 1870s or later
|Austria Calculating Machine
Herzstark & Co.
|Archimedes Calculating Machine
Glashütte, Sachsen, Germany
|Reckoning Machine (a.k.a.
K&E Improved Reckoning Machine,
Peerless Reckoning Machine)
Math. Baeuerle, St. Georgen, Germany
Keuffel & Esser Co., NY, NY (distributor)
1913 Prices $250 (Model 4005), $300 (Model 4006), $375 (Model 4007)
1922 Price $400 (Model 4006)
Stepped-drum. For multiplying large numbers. "The most intricate calculations can
Model 4006, 1922 ad
|Unitas Calculating Machine (a.k.a.
TIM Calculating Machine, Time is Money Calculating Machine)
Advertised 1912-13 (lever set), 1914-24 (keyboard)
Oscar Müller Co. (1912-16) (distributor)
Ludwig Spitz & Co. GmbH, Berlin, Germany
1916 Price $300 and up.
1924 Prices: TIM Lever-Set $300-$450; Unitas Lever-Set $450.
Stepped-drum. Keyboard $50 extra. Electric $300 extra.
Another machine of this type that was sold in 1916 was the Record
(US Adding Machine Co., New York, NY), which was $300 and up
Unitas TIM, lever-set, 1912 ad
Courtesy of the Museum
of Business History and Technology
TIM, lever set
TIM, lever set
Unitas, key set, electric,
TIM, key set
Patented 1892 ~ Manufactured 1895-1935 ~ Marketed in US 1905 ~ Advertised in US
Hans W. Egli, Zurich, Switzerland
1906 Price $400. 1916 Price $400.
1924 Prices: Hand-Operated, Lever-Set $475-$700; Electric Lever-Set,
$835-975; Hand-Operated Keyboard, $575-$825; Electric Keyboard,
1913 ad described the
machine as for "business houses where complex and extended
computations are the rule." 1914 ad stated, "US Government uses 125."
Direct multiplication calculating machine.
|Ensign Electric Calculating
Patented 1904-08 ~ Advertised 1909-24
Ensign Mfg Co, Boston, MA
1910 Price $400 (Model E, 12 places for results), $450 (Model F, 16 places
1916 Price $400
1924 Price $450-$500
Full keyboard, electric, for rapid addition, multiplication and division
As of 1916, this machine had an 81-key keyboard that was used for adding
and a 10-key keyboard that was used for multiplying and dividing.
of the Museum of Business History and
Model E, 1910 ad
Company Founded 1912 ~ On market 1916 ~ Advertised 1917-30
Monroe Calculating Machine Co., Orange, NJ, New York, NY
Full keyboard, crank-operated. Electric introduced 1922.
1916 Price $250
1924 Prices: Crank-Operated $200-$400; Electric $500-$600.
Variable tooth gear.