We, the unwilling, led by the unknowing, are doing the impossible for the ungrateful. We have done so much, for so long, with so little, that we are now qualified to do anything with nothing.
Konstantin Josef Jireček
The British statesman and versatile scientist Charles Stanhope, Viscount Mahon, was a very strange peer—a full of temperament man with enormous mental energies, voice, and earnestness, who devoted a large part of his time and income not to pleasures and parties, but to experiments, science, and philosophy.
Interestingly, in the 1770s the young Stanhope spared a significant part of his time to the developing of calculating machines, devising a total of three calculating devices, as well as a logic machine (so-called Demonstrator). All the calculating machines (so-called arithmetical machines) of Stanhope were manufactured by the skilled clock-maker James Bullock (they are inscribed on the cover: ”Visc(oun)t Mahon Inv(enit) 1780 Ja(me)s Bullock Fecit“ – invented by Viscount Mahon, made by James Bullock), the first machine—in 1775, second—in 1777, and the last—in 1780.
First thought of building a calculating machine appeared to the young Charles Stanhope probably at the beginning of the 1770s, when he studied at the University of Geneva. There his teacher in mathematics was Georges-Louis Le Sage, an inventive man with whom he conducted extensive correspondence. Through him, Stanhope might have heard of earlier attempts to develop such a device, as Pascaline of Pascal and Stepped Reckoner of Leibniz.
The calculating machines of Stanhope typify his obsession with technical innovation whilst retaining a practical, rather than theoretical application. Indeed, he never sought financial reward for any of his inventions—which over time badly drained his fortune—preferring to see them, like his politics, as the practical means to a more enlightened age.
The first calculating machine of Stanhope
In his first calculating machine (made in 1775) Stanhope used the well-known stepped drum of Leibniz, which teeth however are not smooth, but are presented in the form of teeth-strips (strips with 1 to 9 teeth). This type of mechanism will be later used in other machines and will be called adapted stepped drum or adapting segment.
The machine is closed in a fine mahogany case with overall dimensions: 9 x 45 x 17.5 cm, and a weight 9 kg.
The calculating mechanism contains twelve adapted stepped drums (see the photo below), mounted on axes in a special movable carriage. To the axes are attached digital wheels (dials), and to each digit of the dial corresponds a strip of the drum with the appropriate number of teeth (i.e. to digit 0 corresponds the smooth surface of the drum, to 1—a strip with one tooth, etc.).
During the calculations, the carriage is moved, and during this movement teeth-strips will be engaged with the gear-wheels of the main counter and will rotate them according to the teeth of the strip. This action first transfers the entered number into the result mechanism and then performs the tens-carry steps, if needed. There is also a secondary counter, which counters the number of the moving of the carry and is used during multiplication/division. The machine also features a place-shift mechanism to allow multi-digit multipliers and to facilitate division.
During multiplication, the multiplier is set at the beginning and when zero is reached, the multiplication is complete. This course of action also facilitates subtraction and division, as the counter rises from zero to the answer. To prepare the machine for this type of work, a toggle lever at the side is moved until a D appears in the window to right instead of an M. This action reverses the process during the push-and-pull of the carriage: the transfer to the result mechanism now takes place in the second step, with all rotations reversed, and the tens-carry steps are performed in the first step. However, this method of work has the disadvantage that the tens-carry steps arising in the second step are not carried out. Stanhope solved the problem by incorporating an additional small white-handled crank at the left side with which any outstanding tens-carry steps can be done.
The tens carry mechanism of the machine is rather complex and innovative. In fact, Stanhope is the first inventor (although in the sautoir of Pascaline there is something similar), who separated the tens carry operation into two phases: a preparation phase, which is done when the digital wheel rotates from 9 to 0, and the execution phase, which is done during the movement of the carriage. Some 100 years later on this 2-phase operation of tens carry will be widely accepted by the mechanics, because this mode of operation removes the very nasty effect of accumulation of strength in the mechanism.
The second calculating machine of Stanhope
The internal mechanism of the machine from 1777 (see the photo below) is similar to the first machine, as it used again Stanhope’s adapted stepped drum mechanism. However, in the second machine the linear movement, used in the first machine, is replaced by the more convenient and fast rotating movement, so it is more suitable for multiplication and division. The tens-carry mechanism was improved as well.
The second machine of Stanhope is also closed in a fine mahogany case, and was made of brass, iron, and ivory (handles). It’s overall dimensions are: 36 x 22 x 21 cm, the weight is: 9 kg.
Multiplication and division are performed by repeated addition and subtraction with intermediate carriage movements, using a 12-place revolution counter operated by a lever connected to the setting mechanism.
This machine is the first in which tens-carry operation was fully automatic. Whenever one of the figure-wheels at the back is moved from 9 to 0 in addition (or from 0 to 9 in subtraction), a pin projecting from it trips a corresponding spring-loaded tumbler. Below the figure-wheels and tumblers is a shaft. As the cycle continues, teeth on the cam wheel engage a gear on this shaft so that it makes one full revolution; arms on the shaft sweep round and reset any tumblers that have been tripped, and in doing so move the next figure-wheel to the left by one place. The arms on the shaft are set in a helical pattern, so that these carrying operations take place one after another from right to left, allowing for the possibility that one carrying will lead to another in the next place up. Two sets of arms are fitted, spiraling in opposite directions, and two sets of teeth on the cam wheel make the shaft rotate at two different times during the rotation of the drum. These duplications ensure that the carrying operation is fully performed, whether the machine is rotating forward for multiplication or backward for division.
Stanhope’s first calculating machine (from 1775) was an innovative device, which has however several flaws, but by creating his thorough second machine in 1777, he demonstrated that he was able to build an elaborate and fully functional 4-species device. Thus he counts as one of the most innovative inventors of mechanical calculators of the 18th century.
The prototypes of the first two calculating machines of Stanhope were eventually acquired by Charles Babbage, passed down to his son Henry P. Babbage, and given by him to the Victoria and Albert Museum in London in 1905. Besides these two machines, kept now in Science Museum, London, another device survived to our time, and is kept at the Stanhope’s mansion in Chevening, Kent.
Despite using the stepped drum of Leibniz, Stanhope’s first and second machines are quite different from earlier machines in nearly every respect, and seem an original invention.
The third calculating machine of Stanhope
Interestingly, the last calculating machine of Stanhope (from 1780) is the simplest of his three devices, being a small and simple adder. The only surviving to our time example is kept now in the collection Museum of the History of Science, Oxford. The device resembles the earlier adding machine of Samuel Morland.
The third calculating machine of Stanhope was a small and simple adding device with dimensions: 2.2 x 23.2 x 7.5 cm, and a weight about 900 g.
Stanhope’s adding device has 12 digital positions (dials). The first eight (leftmost) dials are decimal and are labeled HM for hundred million, XM for ten million, M for millions, HT for hundred thousand, XT for ten thousand, T for thousands, H for hundreds, and X for tens. The next four dials are labeled L for pounds, S for shillings, D for pence, and F for farthings. This is the old English system of money, used until 1971 (4 farthings = 1 penny, 12 pennies = 1 shilling, 20 shillings = 1 pound sterling).
The rotating of the dials and entering of the numbers is done by means of a stylus, which can be put in the openings in the periphery of the dials. The dials are successively connected within the mechanism by means of wheels with just one cog, thus the tens carry mechanism was difficult to use, having a problem with the transfer of forces.
The Demonstrator of Charles Stanhope
Charles Stanhope worked on his logic machines for some 30 years, creating several versions. On the lower image is shown a circular version of his Demonstrator, created in the late 18th century.
The most effective version of the device was the rectangular one (see the lower image), created at the beginning of the 19th century.
Stanhope’s Demonstrator was designed as a device able to solve mechanically traditional syllogisms, numerical syllogisms, and elementary probability problems. The rectangular version of the device consists of a brass plate (size 10 x 12 x 2 cm), affixed to a thin mahogany block. On the brass face, along three sides of the window, integer calibrations from zero to ten were marked. In the center, there is a depression (4 cm in area and 2.5 cm deep), called the holon. Across the holon two slides can be pushed; one, set in a slender mahogany frame, is of red transparent glass and works through an aperture on the right. The other is of wood, and is called the gray slider. In working the “Rule for the Logic of Certainty” this slide is passed through an aperture to the left; but in working the “Rule for the Logic of Probability”, it is drawn out and inserted in an aperture at the top, when it works at right angles to the red slide.
To solve a numerical syllogism, for example:
Eight of ten A’s are B’s; Four of ten A’s are C’s; Therefore, at least two B’s are C’s.
Stanhope would push the red slide (representing B) eight units across the window (representing A) and the gray slide (representing C) four units from the opposite direction. The two units that the slides overlapped represented the minimum number of B’s that were also C’s.
To solve a probability problem like:
Prob (A) = 1/2; Prob (B) = 1/5; Therefore, Prob (A and B) = 1/10.
Stanhope would push the red slide (representing A) from the north side five units (representing five tenths) and the gray slide from the east two units (representing two tenths). The portion of the window (5/10 x 2/10 = 1/10) over which the two slides overlapped represents the probability of A and B.
In a similar way the Demonstrator could be used to solve a traditional syllogism like:
No M is A. All B is M.
Therefore, No B is A.
The Demonstrator had obvious limitations. It could not be extended to syllogisms involving more than two premises or to probability problems with more than two events (always assumed to be independent of one another). Any of the problems it could handle were solved easily and quickly without the aid of the machine. Actually, Stanhope designed his devices for demonstration purposes, as can be seen by the name Demonstrator, not for solving real-life problems. He wrote “As the instrument is so constructed as to assist us in making demonstrations, I have termed it Demonstrator. It is so peculiarly contrived as likewise to exhibit symbolically those proportions or degrees of probability which it is the object of the Logic of Probability to discover”.
Stanhope bases his system on what De Morgan will call later the arithmetical view of the proposition; and this view determines the form of his method of mediate inference and leads to an extension of the common doctrine. He proposed a rule “for discovering consequences in logic”, which is a remarkable anticipation of that given by De Morgan from the numerically definite syllogism.
Nonetheless, Stanhope believed he had made a fundamental invention. The few friends and relatives who received his privately distributed account of the Demonstrator, The Science of Reasoning Clearly Explained Upon New Principles, were advised to remain silent lest “some bastard imitation” precede his intended publication on the subject. This publication never appeared and the Demonstrator remained unknown until the Reverend Robert Harley described it in an article in the journal the Philosophical Transactions in April 1879. Let’s see the article: “The Stanhope Demonstrator: An Instrument for Performing Logical Operations”:
Earl Stanhope’s Demonstrator is much less powerful as a logical instrument than Professor Jevons’ machine, but the former is undoubtedly a distinct anticipation of the latter. It is probably the first attempt ever made to solve logical problems by mechanical methods. Both in his quantification of the predicate and in his solution of problems involving numerically definite propositions, we see the Earl struggling, not unsuccessfully, to escape into some less confined system of logic than that of Aristotle. He shewed little respect for the authority of the ancient logicians. The same reforming zeal which he displayed in politics he exhibited also in the treatment of logic. He brought to the study of the subject a certain independence and originality of thought which led him to examine the foundations of the science for himself. “I intend,” he declared, “to exclude entirely that long catalogue of pedantic words which are now used for the purpose of drawing consequences, and which are, generally speaking, both unintelligible to youth and unfit for men of any age, so far at least as relates to convenient and habitual use. My system of logic will, on the contrary, be found to have the striking advantage of uniting simplicity, perspicuity, utility, and perfect correctness. The science requires to be totally reformed.”
The materials do not enable us to give a complete or systematic account of Stanhope’s views on logic. Even on the working of his Demonstrator we find in his remains no full or formal statement, but only scattered and fragmentary limits, and a very few simple examples. It is possible, therefore, that in the hands of its noble inventor the instrument possessed a range and power somewhat greater than is apparent to us. He attached to it a practical importance; for us it possesses little more than a theoretic or historic interest. “It exhibits the consequences symbolically,” he wrote, “and renders them evident to the mind. With the aid of this instrument the accuracy or inaccuracy of a conclusion is always shewn, and the reason why such consequences must of necessity exist is rendered apparent. As the instrument is so constructed as to assist us in making demonstrations, I have termed it the Demonstrator. It is so peculiarly contrived as likewise to exhibit symbolically those proportions or degrees of probability which it is the object of the Logic of Probability to discover.”
All propositions are reduced by Stanhope to one form, namely, the expression of the identity of two or more things or classes of things. This “method of identification,” as he calls it, is illustrated by numerous examples. For instance, “Hardness belongs to diamonds,” means that ” Some of those things which possess the quality of hardness and all diamonds are identic.” “Some printing presses cannot be worked without great labour,” means that “Some printing-presses are identic with some of those instruments which cannot be worked without great labour.” In these examples, we recognize an anticipation of Mr. George Bentham’s four forms of affirmative propositions, forms which were afterwards adopted by Sir William Hamilton.
Stanhope bases his system on what De Morgan calls the arithmetical view of the proposition; and this view determines the form of his method of mediate inference and leads to an extension of the common doctrine. He proposes a rule “for discovering consequences in logic,” which is a remarkable anticipation of that given by De Morgan from the numerically definite syllogism. It is a noteworthy fact that he does not limit the rule to a special form but puts it forth as embodying the fundamental principle of all syllogistic ratiocination.
The Demonstrator consists of a brass plate 4.5 inches long and 4 inches wide, affixed to a thin block of mahogany. In the centre there is a depression 1.5 inches in area and half an inch deep, called the holon. Across the holon two slides can be pushed; one, set in a slender mahogany frame, is of red transparent glass and works through an aperture on the right. The other is of wood, and is called the gray slider. In working the “Rule for the Logic of Certainty” this slide is passed through an aperture to the left; but in working the “Rule for the Logic of Probability,” it is drawn out and inserted in an aperture at the top, when it works at right angles to the red slide. Stanhope devised several other instruments of various sizes and construction; but they are both less simple and less effective. It does not seem possible for the Demonstrator in its present form to solve very complicated questions. It is constructed for problems involving only three logical terms; but additional slides would increase its range and power. To Stanhope belongs the honour, and it is a very high honour, of being the first (probably) to attempt the solution of logical problems by a mechanical method. There may be some difference of opinion as to how far he succeeded, but there can be none as to the ingenuity of the attempt. The contrivances of earlier logicians, especially the circles of Euler, probably prepared the way; but Stanhope did undoubtedly take a very important step in advance when he constructed his Demonstrator. His conversion of all propositions into the form of identities by means of the quantification of the predicate, and the principle of his mechanical method, namely, that the process of mind involved in the ordinary syllogism and that involved in the numerically definite syllogism are essentially the same, must be regarded as distinct contributions to logical science and as remarkable anticipations of recent discoveries.
The Demonstrator was important mainly because it demonstrated to others, most notably to William Jevons, that problems of logic could be solved by mechanical means.
Biography of Charles Stanhope
The British politician and man of science Charles Stanhope, 3rd Earl Stanhope and Viscount Mahon, was born in London on 3 August 1753, as the second son in the noble and rich family of Lord Philip Stanhope (1714-1786), 2nd Earl of Stanhope, a British peer, Fellow of the Royal Society and a conspicuous figure in the scientific world, and Lady Grizel Hamilton Stanhope (1719-1811). Philip Stanhope (see the lower portrait) married Grizel Hamilton, daughter of Charles Hamilton, Lord Binning, on 25 July 1745 and they had two children: Philip (1746-1763), and Charles.
Charles was sent very young (only nine years old) to Eton College in Windsor, where studied his brother Philip. Unfortunately, Philip, a very talented boy, inherited from his mother’s family the tendency to consumption, which had proved fatal to so many of the Hamiltons. He was removed to the purer air of Geneva, Switzerland, together with his mother, but eventually, he died on 6 July 1763.
Charles now became Viscount Mahon and the heir to the peerage, and, as the only surviving child, was more than ever the object of his parents’ solicitude. They resolved that his health should not be exposed to the English climate, or the care of his mind to the capricious attentions of the English schoolmaster. He was recalled from Eton, and the family decided on settling in Geneva in July 1764.
The family continued in Switzerland for ten years, where young Charles had been educated at Leyden and Geneva under the inspection of the prominent swiss scientist Georges-Louis Le Sage (1724-1803). He learned Greek and French, and applied himself eagerly to mechanics, philosophy, and the higher branches of geometry, but not to the classics and fine arts. At seventeen, Charles won the prize offered by the Swedish Academy for the best essay on the construction of the pendulum.
At age of 20, still in Geneva, Stanhope was already proven as a promising scientist and good athlete (he rode well, played bowls and cricket, and acquired some skills in shooting and skating). In February 1774, Stanhopes set out from Geneva, with great marks of friendship and honour shewn then on leaving notre seconde patrie. They stayed several months in Paris, and in July 1774 they returned to England.
In September of the same 1774, Stanhope proposed to Lady Hester Pitt (1755-1780, see the nearby portrait), his second cousin and a sister to his friend William Pitt the Younger, the future English prime-minister, and was accepted. The couple married on 19 December 1774, at St. Mary the Virgin church in Hayes. Two years later was born their first child—a daughter, who will become the famous British socialite, adventurer, and traveler Lady Hester Stanhope (12 March 1776 – 23 June 1839). Stanhope had two other daughters from this marriage (Griselda, born 1778, and Lucy Rachel, born 1780), before the early death of Lady Hester (Pitt) Stanhope, on 18 July 1780, of complications following the birth of their third daughter.
The death of Stanhope’s first wife was a tragedy for him, for neither his second wife nor his children inspired him with deep affection.
In January 1775, Stanhope was admitted to the Royal Society, to which he had been elected in 1773 before leaving Geneva. Stanhope’s chief interest outside politics was applied science, and he was acquainted with most of the scientific men of his day. The great drawing-room at his Chevening estate was turned into a laboratory.
In 1880 Stanhope became a member of the House of Commons, upon the death of his father in 1786, when he took his place as a Peer of the realm on 7 March 1786.
Lord Stanhope was a very strange peer—a man with enormous mental energies and earnestness, who devoted a large part of his time and income not to pleasures and parties, but to experiments, science, and philosophy. According to the memories of his contemporaries, he was a tall and thin man (he was frequently compared to Don Quixote, whom he resembled not only in appearance, but still more in valour and high-mindedness), who looked pale, but had a very powerful mind and voice and used to wave his arms around a lot when he was explaining things.
In 1781 Charles Stanhope married his deceased wife’s cousin-german, Louisa Grenville (1758–1829), the daughter and sole heiress of the British diplomat and politician Henry Grenville. Louisa was the mother of three surviving sons, the first of them—Philip Henry Stanhope (1781–1855) inherited not only the title Earl Stanhope, but also many of the scientific tastes of his famous father. It was an unhappy marriage, and in the coming years Charles, 3rd Earl Stanhope after 1784, would fall out with all six of his children, become estranged from his second wife, and take up with a music instructor.
Lord Stanhope was most known by his contemporaries as a politician, but his reputation with posterity depends more upon his talent as a philosopher, scientist, and inventor. Politically he was revolutionary, opposed the slave trade, as well as the war against France, which earned him the nickname Citizen Stanhope, and was a supporter of education and electoral and fiscal reforms. His lean and awkward figure was extensively caricatured by his contemporaries.
Stanhope was an active member of the Royal Society. He wrote a very interesting treatise on electricity. The Lord devoted much attention to the means of preserving buildings from fire. Another object, which took a considerable share of Stanhope’s attention was the employment of steam for the propulsion of vessels, for such experiments he expended very large sums. He shared his knowledge with the inventor of the first commercially successful steamboat—Robert Fulton (1765-1815).
Stanhope’s most significant contribution was to the printing industry. He is well known for suggestions for improvement in the construction of the printing press and as an early patron of the stereotype method of printing. He created a printing press with original construction (see the photo below), which will become very popular all over the world in the next century.
Alongside the ‘Stanhope Press’—a sophisticated iron hand-press with a novel lever and screw mechanism which was used to print The Times until the arrival of steam presses, Stanhope developed a system of logotypes and perfected a means of stereotyping adopted by both Oxford and Cambridge University Presses. Characteristically, Stanhope was driven in these projects by a desire to propagate learning through cheaper schoolbooks though they, yet again, placed a severe burden on his own finances. They also exacted a heavy price on his private life.
Stanhope invented also optical lens, which bear his name, and a method for tuning musical instruments.
Chevening House is a large country house in the parish of Chevening in Kent, in southeast England. The house was the home of the Stanhope family for almost 250 years before it was placed in trust for the nation on the death of the 7th Earl in 1959.
Stanhope’s life was thus one of unremitting toil. He died of dropsy in his family seat in Chevening, Kent, on 17 December 1816, and was buried at Stanhope Chantry in St. Botolph Churchyard, Chevening. Friend and foe agreed that in the third Earl Stanhope one of the most striking personalities of his time had passed away. Throughout his life, Stanhope deservedly enjoyed a great reputation for his discoveries in science, and Lalande called him the best English mathematician of his day.