Samuel Morland

The English polymath Samuel Morland invented in the early 1660s a total of three calculating machines: one for multiplication and division, one for trigonometry, and one for addition and subtraction. Morland’s calculating machines were simple but became rather popular and London instrument-makers were still selling Morland’s calculators as late as 1710.

Samuel Morland entered government service in 1653 when he was chosen to accompany a British diplomatic mission to the court of Sweden’s Queen Christina. Christina of Sweden 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 Blaise Pascal, who in 1652 placed at Queen’s disposal an example. This is probably the most important reason, why Morland became interested in the construction of calculating devices.

In his book, The description and use of two arithmetick instruments (published in 1673 in London), Morland described two invented by him 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. The book may also be considered the first comprehensive book in computer literature, as Blaise Pascal published nothing about his own machine, except one 18-page pamphlet in 1644.

The Machina Nova Cyclologica Pro Multiplicatione of Morland

It seems the first calculating machine of Morland, devised probably in 1664, was so so-called multiplication machine, based on the principle of Napier’s bones. The device was described in the above-mentioned book of Morland under the name Machina Nova Cyclologica Pro Multiplicatione (A New Multiplying Instrument).

Morland ordered manufacturing of the device to the famous English mechanics Henri Sutton (London instrument-maker, active mainly between 1650 and 1661) and Samuel Knibb (1625-1674), and the particular machine, shown here, 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 manufacturing. Let’s examine the construction of the multiplication machine.

In fact, the multiplication machine of Morland simplifies only the intermediate products, using the principle of Napier’s rods. There is no automatic or mechanical carry mechanism provided.

The device is made of 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 a manner, that units and tens of the rods are placed on the opposite ends of the circle (see the lower images for a closer view of the mechanism). There are two rows of axes in the device, the upper axes are fixed, while the lower can be rotated. In the row of windows, placed between the two axes can be set numbers, thus it serves as a mechanical memory. To perform a multiplication, the appropriate disk must be removed from the upper fixed axis and to be mounted to the lower working axis. Each of the lower axes is 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 the horizontal direction by means of the key, which can be seen in the 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 the 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 multi-digital, then these actions must be repeated until all digits will be used.

For example, to multiply 23 by 7, the user would first take the discs for 2 and 3, place them on the central posts and close the door so that in the window the number 23 appears (3 in the left-most window and 2 in the left side of the second pair of windows). Then the user would turn the key until the pin on the slider scale pointed to 7. Each time the key is turned the discs are rotated once, which advances the display of the multiplication table for the selected numbers (2 and 3) by one. The windows are constructed so that a number on the leftmost edge of one disc appears next to the number on the rightmost edge of the next disc. The final answer must be obtained by adding the adjacent numbers in the windows, either with pen and paper or, as the inventor suggested, with the help of his instrument for addition. So, to finish the example, after discs 2 and 3 have been rotated 7 times, the numbers in the display window would read: 1 4 2 1. The final result is found by adding the adjacent digits to give 161.

The Machina Cyclologica Trigonometrica of Morland

Most probably in 1664, Samuel Morland invented a device, that can be used for trigonometric calculations, which he called the Machina Cyclologica Trigonometrica. The device was built in 1670 by John Marke (Maker of mathematical and astronomical instruments active in London between 1665 and 1679. Marke worked with Henry Sutton and succeeded him in 1665.) Materials used: silvered brass and silver, dimensions: 330×275 mm. The instrument is housed in an ebony case with a lid and engraved plate.

The trigonometric calculator of Morland allowed the operator to perform trigonometry by drawing out a problem and measuring the solution as with drawing instruments but without the need for pen and paper. It was a set of three rulers set into a divided circle that could be moved about using dials to form a triangle of any shape.

The device was used for determining the value of a trigonometric function (sine and cosine) of a known angle or, vice versa, for finding the value of an angle when its function is known. The instrument consists of a rectangular box holding a disk with a toothed circumference. At the center of the disk are mounted compasses with a fixed arm and a mobile arm rotating with the disk itself. Below are two smaller disks. The left-hand one shows the angle values. Its index is connected to the toothed circumference of the large disk and completes one revolution for every 30° traveled by the mobile compass arm. The right-hand disk shows the linear sine values. Its index is connected to the mobile horizontal rod on the upper half of the box and completes one revolution for every 25 units traveled by the rod on the side channels. The numbering of the horizontal rod and vertical channels basically represents the sine grid or reduction quadrant.

The machine for addition and subtraction of Samuel Morland

The adding machine of Samuel Morland (presented in the book as A new and most useful instrument for addition and subtraction of pounds, shillings, pence, and farthings…) was devised probably in 1665-1666, as four examples of the device survive to our time. The largest models can add up to one million, in either decimals or pounds, shillings, and pence.

The device (materials used are silver and brass), presented a true pocket calculator, measuring only 4 by 3 inches and less than a quarter of an inch thick (122 x 71 x 8 mm), weight 230 g. On 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 (Sir Jonas Moore was an English mathematician, surveyor, ordnance officer, and patron of astronomy, who warmly recommended the machines of Morland). Humphr(e)y Adamson was a very skillful English clock- and instrument-maker.

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 into 4, 12, and 20 parts and are inscribed and used for calculations in the English currency units of the 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 these 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. Below each window is mounted a stop-pin, which is used for limiting the rotation during the adding operation. Over each big dial is mounted a smaller one, which serves as a counter to 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 the 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 counter-clockwise direction, pushing the stylus in the opening below the window, and rotating the dial until it moves below the appropriate number.

The machine doesn’t have a tens carry mechanism, and this made it useless for practical needs. On 16 April 1668 Morland first printed short descriptions of his two adding devices in the London Gazette—As would now be expected, the adding instrument made its way into the pockets of modern young gentlemen (at a price of £3 10s).

Despite the excellent workmanship of the arithmetic devices of Morland, they were not very useful for practical needs, moreover, some of his contemporaries were not so fascinated by their usefulness also. Samuel Pepys (formerly Morland’s tutee at Cambridge from 1650, who did not think much of Morland) wrote in his 1667-8 years diary, that the machine of Morland is very pretty, but not very useful, while the famous scientist Robert Hooke, wrote in his diary for 31 January 1673: Saw Sir S. Morland’s Arithmetic engine Very Silly. The machines of Morland were, however, appreciated by King Charles II and Cosimo III de’ Medici, Grand Duke of Tuscany, which was more important for Morland as a typical courtier–inventor.

Biography of Samuel Morland

Samuel Morland was born in 1625 at Sulhamstead Bannister, near Reading in Berkshire, England. He was the son of Rev. Thomas Morland, a rector of the local parish church.

Morland entered Winchester School in Hampshire in 1638, and in May 1644, as a sizar (i.e. paying no fees but instead doing basic menial labor for the college between his studies) at Magdalene College, Cambridge. In 1649 he was elected a fellow of the society, and stayed there until 1653, but took no degree. While in College, Morland devoted much time to the study of mathematics, but he also became an accomplished Latinist and was proficient in Greek, Hebrew, and French (then the language of culture and diplomacy).

For the latter half of his time at university, Morland was a noted supporter of the Parliamentarian Party, and, from 1647 onward, he took part in student politics. In November 1653, he was included in the retinue of the English lawyer, writer, and parliamentarian Bulstrode Whitelocke, on an embassy to the Queen of Sweden for the purpose of concluding a military alliance. Whitelocke describes him as a very civil man and an excellent scholar; modest and respectful; perfect in the Latin tongue; an ingenious mechanist.

Upon his return from Sweden in July 1654, Morland was appointed as an assistant to John Thurloe, the secretary of the Lord Protector Oliver Cromwell. Later Cromwell appointed him as “commissioner extraordinary for the distribution of the collected moneys” and one of the clerks of the signet. In May 1655, Morland was sent by Cromwell to the King of France and to the Duke of Savoy to remonstrate with him on cruelties inflicted by him upon the sect of Waldenses or Vaudois, which had strongly excited the English public. Morland remained, for some time, in Geneva as an English resident, and his actions were highly appreciated after his return to England in December 1655.

Upon his return to England, Morland became intimately associated with the Government of the Commonwealth and he became a witness to several not-so-legitimate actions of his magnates, e.g. of Dr. Hewitt’s being “trepanned to death” in June 1658 by Thurloe and his agents. The most remarkable intrigue, however, which came to his knowledge was the so-called Sir Richard Willis’s Plot from the beginning of 1659. Its object was to induce King Charles II and his brother to effect a landing on the Sussex Coast, under the pretense of meeting their adherents and putting them both to death the moment they disembarked. This plot is said to have formed the subject of a conference between Cromwell, Thurloe, and Willis at Thurloe’s office, and the conversation was overheard by Morland, who pretended to be asleep at his desk. From this time, Morland endeavored to promote the Restoration and warned the King about the plot. In justifying to himself the abandonment of his former principles and associates, he observes that avarice could not be his object, as he was, at this time, living in greater plenty than he ever did after the Restoration, having a house well furnished, an establishment of servants, a coach, & co, and £1,000 a year to support all this, with several hundred pounds of ready money, and a beautiful young woman to his wife for a companion (in 1657, Morland married Susanne, daughter of Daniel de Milleville, Baron of Boissay in Normandy).

Morland officially joined the King’s party in May 1660, when in departed to Breda, bringing with him letters and notes of importance. The King welcomed him graciously and publicly acknowledged the services he had rendered for some years past, making him liberal promises of “future preferment” but these were, for the most part, unfulfilled. On 18 July 1660, Morland was made a baronet, being described as of Sulhamstead Bannister, although it does not appear very clear whether he was in possession of any considerable property in the parish. He was also made a Gentleman of the Privy Chamber; but this appointment, he says, was rather expensive than profitable, as he was obliged to spend £450 in two days on attending the ceremonies accompanying the coronation. He, indeed, obtained a pension of £500 from the post office, but his embarrassments obliged him to sell it, and, returning to his mathematical studies, he endeavored, by various experiments and the construction of machines, to earn a livelihood. But the King’s gratitude went no further. Morland was extravagant, sold his pension, wasted the proceeds in France, and ended as a beggar.

In 1666, Morland obtained, in conjunction with Richard Wigmore, Robert Lindsey, and Thomas Culpeper, a probably remunerative patent “for making metal fire-hearths”. From correspondence between Morland and Dr. Pell, it appears that about this same time (1666), the former had intended to publish a work “On the Quadrature of Curvilinear Spaces” and had actually proceeded to print part of it, but was happily persuaded, by Pell, to lay it aside. In carrying out his experiments in hydrostatics and hydraulics, Morland encountered many difficulties as a consequence of their expense. In December 1672, the King granted to him the sum of £260 to defray the charges of about five hundred looking-glasses “to be by him provided and set up in Olive wood frames for our special use and service,” as well as an annuity of £300 “in consideration of his keeping and maintaining in constant repair a certain private printing press… which by our Especial Order and Appointment he hath lately erected and set up”.

In 1681, Morland was appointed “magister mechanicorum” to the King, who, in recognition of his ingenuity, presented him with a medallion portrait of himself, set in diamonds, together with a medal as “an honorable badge of his signal loyalty”. In October 1684, the King advanced him £200 and, a year later, Morland received a similar sum by way of “bounty”.  According to his own account, his mechanical experiments pleased the King’s fancy; but when he had spent £500 or £1,000 upon them, he received sometimes only half, and sometimes only a third, of the cost.

In 1682, Charles II sent him to France “about the King’s waterworks,” but there also he seems to have lost more than he gained. On his return, King James II restored to him his pensions, which had been, for some reason, withdrawn and, likewise, granted him part of the arrears, but Morland was never repaid the expenses of the engine which he had constructed for bringing water from Blackmore Park, near Winkfield, to the top of Windsor Castle. In 1686, Morland was corresponding with Pepys about the new naval gun-carriages. In 1687, his pension was paid down to Lady Day 1689.

In 1689, Morland addressed a long letter to Archbishop Tenison, giving an account of his life, and concluding with a declaration that his only wish was to retire and spend his life “in Christian solitude”; and he begs the primate’s “helping hand to have his condition truly represented to his Majesty.” Tenison probably did something for him, as there is a letter of thanks for “favours and acts of charity,” dated 5 March 1695. The errors of his life were probably considerable, as he speaks of having been, at one time, excommunicated; but some of his writings show that he was a sincere penitent, particularly ‘The Urim of Conscience’ (1695), written, as the title says, “in blindness and retirement.”

Morland married four times but was definitely not happy in his family life. In 1657 he married the Huguenot Susanne de Milleville, the beautiful daughter of Daniel de Milleville, seigneur de Boissay, Commissaire du roi au syndic provincial de Normandie, and Catherine de la Wespierre, his wife. They had three children (one son, Samuel), but Susanne died in 1668, when she returned with the children to France, mortally ill with dropsy (In his Sep. 1667 diary Samuel Pepys mentioned that they went to King’s Play House and …Here we saw Madam Morland, who is grown mighty fat but is very comely.)

Morland married secondly, on 26 October 1670, in Westminster Abbey, Carola Harsnett (1651-1674), daughter of Sir Roger Harsnett, knight. They had two children, but Carola died on 10 October 1674, aged 22. Morland married thirdly, on 10 November 1676, in Westminster Abbey, Anne Fielding (1661-1680), third daughter of George Fielding of Solihull, Warwickshire, by Mary, second daughter of Sir Thomas Shirley, knight, of Wiston, Sussex (Anne died on 20 February 1680, aged 19, leaving no issue). Lastly, Morland married, at the Knightsbridge Chapel, Middlesex, on 1 February 1687, Mary Ayliffe, a woman of low origin and infamous character, from whom he obtained a divorce for adultery on 16 July the following year.

Morland lost his sight about three years before his death. He died on 30 December 1695 and was buried in the Hammersmith Chapel on 6 January 1696. He must have been in an extremely weak condition, as he was unable to sign his will. By it, he disinherited his only son, Samuel (died Nov. 1716), who was the second and last baronet of the family, as the reason for this appears from a passage in a letter “I have been, in my youthful days, very undutiful to my parents, for which God has given me a son, altogether void of filial respect or natural affection”.