In 1867, Frederick A. P. Barnard, a mathematician and the president of Columbia University in New York, served as a judge at the Exposition universelle, a world’s fair held in Paris. There he saw a calculating machine for the first time. In a report on the fair, Barnard wrote:
To most persons the process of calculation involves a species of mental labor which is painful and irksome to the highest degree; and to such, no part of their educational experience recalls recollections of severer trials [sic], or of burdens more difficult to bear. That this toil of pure intelligence – for such it certainly seems to be – can possibly be performed by an unconscious machine is a proposition which is received with incredulity; and even when demonstrated to be true, is a phenomenon which is witnessed with unmingled astonishment.
He promptly arranged for Columbia to purchase of one of these astonishing machines for his office.
By 1900, calculating machines were not unusual wonders. Entire companies in Europe and the United States manufactured them. The machines served as common tools of scientists, engineers, statisticians, actuaries, government officials, and payroll clerks. Business students learned to use them in school. With the introduction of inexpensive electronic calculators in the 1970s, calculating machine manufacture ceased and the devices became hefty reminders of a bygone era.
While calculating machines are no longer commonly used, they remain curious as fine mechanisms, as evidence of the growing role of numbers in modern life, as products of industry (especially in Europe and the United States), and as examples of industrial design. They well illustrate the international diffusion of ideas, the place of immigration in invention and manufacture, and the importance of labor shortages in creating new roles for both women and machines. A few companies that sold calculating machines, such as Remington Rand, Monroe, Friden, and SCM Marchant, also influenced the early development of electronic calculators and computers.
Calculating machines, narrowly defined, are devices designed to add, subtract, multiply and divide through the motion of their parts, with the result represented by an array of digits. A slightly wider definition of the term includes machines designed especially for addition (and sometimes subtraction). Here these are called adding machines, and discussed in a separate object group of that name.
The two most common mechanisms for calculating machines are the stepped drum and the pinwheel. Machines of these types are discussed in the first two sections. Early machines of these kinds multiplied, in part, by repeated addition. A user set the number to be multiplied and wound the crank as many times as the rightmost (ones) digit of the multiplier. The operator then shifted the carriage one to the left and wound the crank the number of times equal to the tens digit. Continuing the process allowed an entire multiplication. From the 1870s, machines were designed on which digits of the multiplier could be set, and the crank wound only once for each digit. Such direct multiplication machines, as well as those on which one could multiply entirely automatically, are discussed in the third section. The fourth section discusses a variety of calculating machines with other designs. The final section describes the earliest printing calculating machines, which were specifically designed to compute and print mathematical tables by evaluating polynomials. These machines, called difference engines, have received considerable attention from historians of computing.