The Calculating Machines of Sir Samuel Morland

The polymath Samuel Morland (biography), was a notable English academic, diplomat, spy, inventor and mathematician of the 17th century, credited with early developments in relation to computing, hydraulics and steam power.

Morland entered government service in 1653, when he was chosen to accompany a British diplomatic mission to the court of Sweden's Queen Christina. The Swedish queen was a noted patron of the sciences, and it was most likely at her court that Morland first became acquainted with the calculating machine of Pascal, who had presented Christina with an example in 1649. This is most probably one of the reasons, that some 10 years later, Morland to construct three calculating devices.

In his book—The description and use of two arithmetick instruments, published in 1673 in London, he describes two invented calculating devices, which are working without charging the memory, disturbing the mind, or exposing the operations to any uncertainty. This is the first book on a calculator, written in English, and the first separate work on the subject after Napier’s Rabdologiae. There was little else in English on calculating instruments for more than 160 years from this book and the publication of Babbage in 1827. The book may also be considered the first comprehensive book in computer literature, as Blaise Pascal published nothing about his own machine, except an 18-page pamphlet in 1644.

The description and use of two arithmetick instruments of Morland

The arithmetical machines of Morland were produced around 1666 and were presented to the King Charles II and general audience. First machine is a simple adding device, similar to the device of the italian Burattini, produced some years earlier (see the photo bellow).

The adding device of Morland

The device presented a true pocket calculator, measuring only 4 by 3 inches and less than a quarter of an inch thick (100 x 80 x 7 mm). On the page 12 of the book Morland advertises that the instruments may be ordered from Humphry Adamson, living at Jonas Moore’s house in the Tower.

On the lid of the device are mounted 8 pairs of graduated dials. The scales of the dials are inscribed on the ring around them. The lower three scales are divided to 4, 12 and 20 parts and are inscribed and used for calculations in the english currency units of 17th century—guinea (which was equal to 20 shillings), shilling (which was equal to 12 pennies), and penny (which was equal to 4 farthings). The upper five big dials have decimal scales, and are inscribed with words unit, tens, hundreds, thousands, tenth.

Across the periphery of each big dial are made openings, according to the scale of the dial—4, 10, 12 or 20. In this openings can be put a stylus, and the dial can be rotated. During this rotation, in a little window in the upper part of each scale can be seen the appropriate number. Bellow each window is mounted a stop-pin, which is used for limiting the rotation during adding operation. Over the each big dial is mounted smaller one, which serves as a counter of the revolutions of the big dial. For that purpose is used one-toothed gearing—the lower dial has one tooth, while the upper dial has ten teeth, so making a full revolution of the lower dial has as a result 1/10 revolution of the upper one.

The adding operation is performed by rotating the appropriate dials in the clockwise direction, pushing the stylus into the opening against appropriate number and turning the dial until the stylus will be stopped by the stop-pin. The subtraction can be done by rotating dials in the counterclockwise direction, pushing the stylus in the opening bellow the window, and rotating the dial until it moves bellow the appropriate number.

The machine doesn't have tens carry mechanism.

The multiplication machine of Morland (© Istituto e Museo di Storia della Scienza, Florence)

Second of the machines of Morland—so called multiplication machine, is based on the principle of Napier's bones (see the upper photo). This particular device was manufactured for Morland by the famous english mechanicians Henri Sutton and Samuel Knibb (the other calculating devices of Morland were fabricated by the skilful mechanician Humphry Adamson), and was donated by Morland himself to Grand Duke Cosimo III de' Medici in 1679. The dedication to the Grand Duke contains an obvious error: it gives 1666 as the year of invention and 1664 as the year of manufacture. Let's examine the construction of the multiplication machine:

The sketch of the multiplication machine of Morland from his book The description and use of two arithmetick instruments (© United States Library of Congress)

The skilfully produced device is made by silver, gilt and silvered brass, wood and crystal. The dimensions are 18 x 55.5 cm.

The digits from the ten Napier's rods are inscribed across the periphery of 10 thin metal disks in such manner, that units and tens of the rods are placed on the opposite ends of the circle (see the nearby and lower images for a closer view to the mechanism). There are two rows of axis in the device, upper axis are foxed, while the lower can be rotated. In the row of windows, placed between the two axis can be set numbers, thus it serves as a mechanical memory. To perform a multiplication, appropriate disk must be removed from the upper fixed axis and to be mounted to the lower working axis. Each of the lower axes has attached to a small pinion in the body of the machine, and this pinion is engaged with a toothed strip. This strip can be moved in horizontal direction by means of the key, which can be seen in lower right part of the lower figure, and its movement is marked by an arrow, which can be moved across a scale.

When the appropriate disks are set (according to the digits of the multiplicand), the lower part of the machine is covered by a lid, which has windows. The key must be rotated by the operator, until the arrow comes to the digit of multiplier on the scale, and during this rotation the toothed strip will move and rotate the pinions, engaged with it. Thus in the lower row of windows can be seen the product. If the factors are multidigital, then this actions must be repeated until all digits will be used.
Actually, the multiplication machine of Morland simplifies only the intermediate products, using the principle of Napier's rods.

Later on, Morland invented a device, that can be used for trigonometric calculations (see the nearby photo).

Despite of the excellent workmanship of the arithmetic devices of Morland, his contemporaries were not so fascinated by their usefulness. A friend of Morland (Samuel Pepys) wrote in his 1667-8 years diary, that his machine is very pretty, but not very useful, while the famous scientist Robert Hooke, for example, found the machines very silly.