Antique Mechanical Computers – Part 1: Early Automata (Jul, 1978)

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Antique Mechanical Computers – Part 1: Early Automata

Dr James M Williams
58 Trumbull St
New Haven CT 06510

My purpose in writing these articles is to remind computer enthusiasts that there is a high technology in every age, not just our own. Described herein are some of the stellar accomplishments of earlier times. The technology of electronics is merely the latest link in a continuous chain of technological developments spanning 20,000 years. Before that, there was a mechanical technology.

Part 1 of this three part series describes some highlights in the development of automata up to the 18th century. Part 2 continues with 18th and 19th century developments, and part 3 concludes with a description of Torres’ 1911 chess automaton.

I am not going to speak here of those incandescent moments long ago when the truly great and critical achievements of mechanics were discovered: that day when an ancient man hooked a stick under one large stone and over another to invent the lever. Nor will I consider the wheel, which, however it came about, multiplied mechanical possibilities so manyfold (pulley, cam, gear, crank, escapement) that as the knowledge spread humanity was irrevocably changed. We simply do not know the story of mechanical knowledge and its spread, so we must spin scenarios instead of histories. We will also have to concentrate on highlights, since an exhaustive treatment of mechanical computers would fill many books.

We do know most of the latest chapter, however. It has taken place in the past 350 years, beginning in Renaissance times, flourishing in the Industrial Revolution, and finally levelling off in the early years of this century. The mechanisms that are now commonplace were being born back then, and what exciting times they must have been. Glance through a compilation of mechanisms and note the dates of first appearances in machinery. You will be surprised to see how many basic movements date from two centuries ago. And with study and application, a man could learn them, make them his own, and employ them in mechanisms of his own. Consider the thrill of the obscure local blacksmith in, say, Saxony 400 years ago who copied in wood the mechanism of the town clock’s striking-jack — the clock, a wonder that was the envy of other towns, imported at great expense from Italy — and discovered for himself the means of transforming rotary motion into intermittent linear motion, via a cam. (Medieval cathedral clocks generally had a life-size figure, man, angel, or devil, which carried a mace to strike hours on a bell: the “striking-Jacques” or “striking-jack.”) Imagine the challenge and excitement in realizing that one could construct a clock that would strike noon fairly consistently when the shadow of the church steeple touches a particular joint of flagstone in the village square. Could one compress this wonderous mechanism into a container small enough to carry, and be able to see the time whenever he wished? Could one construct a clock for the pocket?

The first ones showed up around 1650, bulky as an ostrich egg and not much better at keeping reliable time. A little over two centuries ago a carpenter from Yorkshire, England, James Harrison, who had taught himself mechanics over a period of 30 years, constructed his fourth highly accurate watch (chronometer) and won a prize of £20,000 from the British government in 1760. Determined to make the British Navy the master of the seas, the Admiralty offered a prize for a watch that would permit a ship to calculate its longitude with an accuracy of 60 nautical miles after being at sea for six weeks. (Latitude is relatively easy to calculate by accurately measuring the elevation above the horizon of any celestial body. Longitude is more difficult, and requires knowing the elevation at a time known relative to a fixed reference, the zero meridian at Greenwich, England.) Mechanicians (an excellent name for the practitioners of this craft) chose to work in the field for much the same reasons we all choose a field today: because it was an absorbing and genteel means of earning a living, because it offered accomplishments one could show with pride, and because it was the area for future expansion, the growing edge of the technology. Look at the legacy of machines they have left us: the Linotype, the typewriter and its relatives, the reproducing piano (and its less intelligent cousin, the player piano), clocks and watches of every description. They are all fine mechanisms, but most of them were perfected and essentially attained their present configuration 80 years ago and more. Electronic devices have displaced most of them.

The flowering of mechanical technology had other branches that have now died out, though, leaving only accounts in books and a few decaying museum specimens of machinery which once stirred general admiration and brought fame to their creators: the Orrery, a clockwork model of the solar system, complete with moons, that once stood proudly in the exhibition room of every significant university; the dazzling variety of music boxes which once were found in every parlor; and so on. And who nowadays recalls the bird organ (see photo 1 and figure 1)?

The bird organ was a mechanical device that produced a very close simulation of a bird’s song; 200 years ago it was a very expensive and much cherished ornament in the parlor of every gentle home. I have seen electronic versions of circuits for such a device and have built one, but together with its transformer and loudspeaker it occupies most of the space in a small bird-house. A commercial version I purchased is slightly smaller, housed in a 3 inch plastic sphere. Around the year 1800 there was a bird organ made for sale to replace the head of a gentleman’s walking stick. A hinged lid sprang open by a concealed catch, and out popped a minute feather covered bird model that opened its beak, spread its wings and sang. The entire device, except for its winding key, was housed in a gold ornamented cylinder 154 by 2 inches (3.8 by 5 cm) long. How’s that for miniaturization? And I’ll wager it made a better song than my blocking oscillator version.

There were bird organs, or accounts of them, in antiquity. The Greeks used steam or air to drive whistles mounted in bird figures; the Arabs and Persians supposedly did the same. The mechanism was sometimes a cluster of tuned whistles like a bank of miniature organ pipes, and this arrangement is found in a clock from 1750, but the modern bird organ dates from about 1770 and was likely devised as a means of teaching domesticated songbirds to sing. Soon miniaturized, it was incorporated into decorative objets d’art of all sorts: snuff boxes, perfume flasks, table centerpieces (these often had small fountains of water and other distractions built in), clocks, even watches (but these were very rare), and free standing forms. One delightful version of the latter, perhaps 9 inches (23 cm) high, depicts a lady seated at her desk and a bird on a perch pole nearby. Her hand is on a (mock) bird organ, which she cranks while her pet listens attentively. The bird then tries to copy the song, but makes errors, which she corrects by playing the lesson again so that the bird “learns” and repeats it accurately, with much enthusiastic flapping of wings, pivoting on the perch, etc.

Large or small, the mechanism of bird organs was always the same (see figure 1): a main spring drove a gear train which operated a bellows to compress air in a wind box, and another gear train drove an intricately cut cam which, via a piston, varied the pitch of a whistle connected to the air supply. A similar cam operated a valve to control the volume of the whistle tone. More gears drove cams that controlled the beak, wings, and pivoting actions via push wires ascending the perch pole and the bird’s hollow legs. Songs of eight or nine species are to be found among bird organ mechanisms (some elaborate devices had double or triple songs), and the nightingale was most popular. Remember the fairy tale about the mechanical nightingale by brothers Grimm, about 1855? It lived in a jewelled tree, and some devices were made in this form, but the objet d’art was perhaps most popular, being finished in enamel and gold and frequently decorated with precious stones. While bird organs were essentially one of a kind machines, there was a sort of production line for them maintained by the most famous makers, and many thousands of them exist in museums. A great many were exported from France and Switzerland to the Orient. They are still made, and, while expensive, they are no longer the luxury of rich men. [A German bird organ about the size of a pocket calculator is currently available for under $400 ... CM] In computer terms, the complete mechanism might be described as a spring driven power train controlled by a mechanical read only memory whose values are stored as a distance of the edge of the cam from the cam’s center of rotation. In 45 seconds of singing, there might be a fair number of places where the notes sound, perhaps, six to eight per second (during a trill).

Referring to figure 1, if we have two cams which rotate in 45 seconds, and we allow a time division of ten samples per second, and if we allow eight bits of precision per sample, we would require 900 bytes of read only memory to simulate the control functions of these cams.

A longer song, as in the tutorial automaton described above, might require three times as many bytes together with a smaller number to control bird and figure motion. This gives a total of 3 K bytes of mechanical read only memory divided unequally among several cams (something approaching the storage capacity of contemporary read only memory parts).

A better way to look at this sort of mechanism might be as a computer with analog storage (varying cam curves) and analog output (varying positions of the volume valve and pitch piston). Information is stored in the intricate curves of the cams. The information is fixed there for all time, or until wear or rust alter it, and may be recovered whenever it is needed by rotating the cam while the cam-follower rides on its periphery. It is in every way an “analog” of the desired sound, but it is not a recording, because it has been distorted in storage to suit the particular readout mechanism being employed (the cam-follower). (I have described the stored information as digital in order to facilitate the comparison; this has validity because of the relatively small number of analog positions and their re-solvability into bytes of restricted number.) Even in the 1770 to 1850 era the cam was not a new invention, but this application was novel. It was a benchmark in the field of mechanics. Storage of information had now become a tool of the mechanician, where formerly mere repetitive movement, the regular back and forth movement of a clock’s mechanism, was known to be available.

With the possibility of storing information comes the possibility of crafting complex and seemingly nonrepetitive movement. If it is the desire of the builder of the mechanism, these movements may be arranged to mimic the movements of living organisms. This is the basis of more complex mechanical toys like the rabbit that walks about beating on a drum. (Incidentally, in 1880 a minute gold rabbit, perhaps an inch high, who also played his drum, was sold as a brooch. Not to mention a 3 inch gold caterpillar that sedately crawled its path, circa 1850.) However engaging, these were fundamentally simple and regular movements that did not tax the designer. Mechanicians have constructed far more complex machines designed to duplicate the most intricate and coordinated movements performed by living creatures and to produce an effect of illusory life for the few minutes the mechanism operates. Why would clever, dedicated people do such a thing? Why build an automaton?

Machines That Imitate Life: a Rationale Until modern times there was a pervasive and unchallengeable view that the bodies of human beings were not fit subjects for investigation. Death was the penalty for human dissection during the middle ages, except for rare occasions when the Church sponsored demonstrations of the corpses of criminals. Clearly, anything so sternly forbidden must have been well worth investigating; could it have been that the secret of life lay concealed in the structure of the body? There were some who took the risk, and they always found that animal and human structure were very similar. Since, in the influential and respected view of Rene Descartes (1596-1650), animals were machines that differed from humans chiefly in their lack of divine inspiration, it is easy to see the framework for a “mechanistic” view of living organisms. The notion held much appeal. It explained in terms that were comprehensible to the average educated man how living creatures were constructed by substituting mechanism for mystery.

Popular expositions of science from the 1890s right up to the 1940s typically depicted drawings of a person cut away to reveal bellows and pump rooms in the chest, the chemical factory in the abdomen, the telephone switchboard in the skull, the pistons and gears in the limbs, and so on.

I suggest that this conception of organisms as chains of mechanisms, and the corollary, of a god as the divine watchmaker who constructed and set them in motion, was perhaps the most influential factor leading to the construction of machines designed to imitate life. Note the variety of literature in which the attempt to create life is central to the theme: from ballads and fairy tales dating back to the beginning of language to Mary Shelley’s Frankenstein (1818); from Offenbach’s opera with the clockwork ballerina, Tales of Hoffman (1881), through countless science fiction works, to tales such as Shaw’s Pygmalion. And of course there is recombinant DNA research, the leading edge of biochemical investigation at this moment where the purpose is, manifestly, to explore the mechanisms of life in living cells. The impulse is still there in us although the metaphor is different in different ages, and the mechanisms employed are dependent on available technology.

Astonishing Automata About 1709, in Grenoble, the Edison of automata, Jacques de Vaucanson, was born. Little is known of his early life, except that he was something of a rake and a seminary dropout who disrupted affairs at the monastery by making wood and paper wings that flew about. But much is remembered of his automata, which, though they no longer exist, were the marvel of their age, the object of admiration by all gentlemen who saw them, and the envy of mechanicians ever since.

Vaucanson was not a showman, but a philosopher and inventor. He often spoke of “moving anatomy,” his expression for the concept that life, especially life in lower animals, was in fact a series of undirected movements (what we would today call “reflex movements”), and that by duplicating the movements and actions of a live creature, one might succeed in duplicating the life of the creature. While such a notion seems absurd to us (it is, according to current understandings of the formation of ideas, magical, and therefore primitive) there is precedent for it from a character no less important than St Thomas Aquinas. Vaucanson had a splendid opportunity to come across St Thomas’s writings, since he lived in a monastery for perhaps 15 years. Books were expensive treasures in 1709, and monasteries were the main places where collections existed. St Thomas’s works would probably have been among them. In the Summa Theotogica (Q13; Art 2; Reply obj 3; Part II) there is a passage: “Animals show orderly behavior and are machines, as distinct from man who has been endowed with a rational soul and therefore acts by reason.”

If animals are orderly machines, it might be possible to make a machine that looks and behaves like an animal. If one took special pains to reproduce vital details like respiration, digestion and excretion, etc (so runs the argument), one would then have created the next best thing to a real living animal.

Vaucanson arrived in Paris in 1735 at the age of 26 to pursue his moving anatomy con- cepts. He promptly ran out of money. There is documentation to show he had the idea “. .. of getting assistance by producing some machines that could excite public curiosity .. .” as a means of raising funds. He excited plenty of public curiosity, for in 1738 he simultaneously displayed three automata (see figure 2a). An automaton duck “. . . made of gilded copper who drinks, eats, quacks, splashes about on the water, and digests his food like a living duck” was one, and a pair of automata musicians who played flute and drums were the others.

The machines were life-size and were mounted on cubical pedestals about three feet on a side, which contained the bulky mechanism. They were unique and original, and they created a public sensation for 50 years. To me, the flute player seems the most remarkable mechanism of the three. De Juvigny, a friend of Vaucanson’s, wrote in 1777, “At first many people would not believe that the sounds were produced by the flute the automaton was holding. These people believed that the sounds must come from a bird organ or German organ enclosed in the body of the figure. The most incredulous, however, were soon convinced that the automaton was in fact blowing the flute, that the breath coming from his lips made it play and that the movement of his fingers determined the different notes. . . The spectators were permitted to see even the innermost springs and to follow their movements.” Figure 2b shows the mechanism in outline form. All that needs mention is the weight motor (not shown), and the fact that different weights were added to each bellows in the set of three to provide different pressures of air. High, medium and low pressures provided the designer with the possibility of playing notes loudly or softly in the lowest register, or of shifting the flute to a higher register by employing greater pressures. The distributor valve selected the correct pressure for a given note.

The illustration merely hints at the head mechanism, which must have been extremely complex. This description of flute playing is from the Encyclopedia Brittanica: “The flute is held sideways to the right of the player, who forms his lips to make an aperture and directs his breath stream across the mouth hole and onto its further edge, where it breaks up into eddies that alternate regularly above and below this edge and so excite the air column of the flute into vibration. Stability of the notes in the various registers and at different loudnesses is achieved by control of lip aperture, angle of breath impact, and breath force. The compass is three octaves. …” Vaucanson’s complications came from his decision to use the true flute, blown from the side, and not a recorder, which is an air pipe instrument blown from one end like a pennywhistle or organ pipe. In both instruments, air column length is varied by closing the appropriate holes in the body. To some degree Vaucanson simplified his task by employing seven active fingers (instead of eight, the modern standard: or maybe his particular flute had only seven fingerholes), but he took on and overcame the challenge of providing means to produce the proper size of lip aperture and the proper angle of breath stream to mouth hole. It seems quite likely that Vaucanson used actual rubber, first seen in France in 1736, in the lip mechanism, for there is evidence (in another automaton) that he knew how to fabricate rubber.

Now, I can imagine a mechanism that would dilate and contract the aperture in a set of rubber lips, and vary somewhat the angle of a stream of air blown through the hole, but I have the considerable advantage of being able to draw on two centuries’ accu- mulation of mechanical knowledge. Vaucanson was starting from scratch, building a mechanism never before seen, to produce a motion never before defined, to perform a task never before attempted. That he succeeded so well is astonishing; that he did it within 36 months is staggering. And remember, he employed mainly hand tools. There was no local machine shop he could call on to mill a part. We have no record of where Vaucanson learned his mechanics, but his skills were prodigious.

The combination tabor (drum) and flageolet (pennywhistle) player shown at the right in figure 2a was undoubtedly constructed along similar lines; I have not seen an explanation of its mechanism. It would have been simpler, since the flageolet is easier to play than a flute (only four or five finger holes, blown from one end), and machinery to make the right arm beat the drum would be relatively simple to figure out. It seems unlikely the two automata could have been so well synchronized that they played together.

Vaucanson’s Mechanical Duck It always startles me to read things like this anonymous appreciation of Vaucanson’s duck: “It is the most admirable thing imaginable, a piece of human worksmanship almost passing understanding.” I try to account for the powerful attraction that constructing simulacra of lower animals held for men 200 years ago. Still, it catches me off guard to see the adulation the duck evoked. Dr G C Beireis, the fourth owner of the machine in 1785, rhapsodizes, “It was in this duck that Vaucanson’s genius reached its highest point. I have still not got over my astonishment at this work. (He had seen it thirty years earlier.) One single wing contains more than 400 articulated pieces.” I doubt we would feel that way today about an automated Scottie, say, but maybe ducks make better pets.

It was, from all accounts, a singular likeness to a duck, and here is what it did: After a light touch on a point on the base, the duck in the most natural way in the world begins to look around him, eyeing the audience with an intelligent air. His lord and master, however, apparently interprets this differently, for soon he goes off to look for something for the bird to eat. No sooner has he filled a dish with oatmeal porridge than our famished friend plunges his beak deep into it, showing his satisfaction by some characteristic movements of his tail. The way in which he takes the porridge and swallows it greedily is extraordinarily true to life. In next to no time the basin has been half emptied, although on several occasions the bird, as if alarmed by some unfamiliar noises, has raised his head and glanced curiously around him.

After this, satisfied with his frugal meal, he stands up and begins to flap his wings and to stretch himself while expressing his gratitude by several contented quacks. But most astonishing of all are the contractions of the bird’s body clearly showing that his stomach is a little upset by this rapid meal and the effects of a painful digestion become obvious. However, the brave bird holds out, and after a few moments we are convinced in the most concrete manner that he has overcome his internal difficulties. The truth is that the smell which now spreads through the room becomes almost unbearable. We wish to express to the artist inventor the pleasure which his demonstration gave to us. (From Chapuis’ book, Automata: Historical and Technical Study, see detailed bibliography in part 3 of this article.) Something here for everyone, isn’t there? Passion, satisfaction, and a dash of slapstick. The mechanicians in the audience were dazzled by Vaucanson’s skill in building a duck that could swivel its neck in every direction while sitting or standing; this does suggest some remarkable techniques for managing the pushwires ascending the legs, maybe even some internal mechanisms within the body.

Probably written by Vaucanson and certainly based on data only he could have provided, the following passage from an article in a 1777 dictionary of science shows how proud he was of the internal mechanisms that caused grain to be “. . . digested as in real animals by dissolution and not by (grinding) … the inventor does not set this up as a perfect digestive system capable of manufacturing blood and nourishing juices to support the animal, and it would be unfair to reproach him with this shortcoming.” But it is clear how well he knew the 18th century idea that blood comes from food, and he implies he was trying to follow it. Indeed, in some accounts the body was covered by latticework so the interior mechanisms could be viewed as they did their job. Vaucanson had good reason to be proud, for the body contained his new invention, the rubber tube. Any machine capable of making that kind of smell had to be alive!

One wonders what the “…chemical laboratory where the principal part of the food could be decomposed…” mentioned in the article might refer to. It may have been that his rubber tube intestine actually contained some chemicals or enzymes that attacked the starch in oat porridge, causing it “…to leave the body in markedly changed form.” But there was hardly time enough in a performance of a few minutes to convert anything. More likely the operator between performances drained the stomach of its contents and loaded the nether-part of the intestine with the imitation duck dung that so impressed audiences.

The duck and the two musicians probably made a good deal of money for Vaucanson, but because it was necessary to transport them to other capitals of Europe for further exhibition he sold them all in 1743 to showmen who took them to England, Russia, and finally to Germany. In St Petersburg in 1 782 the third owners tinkered with the mechanisms, interchanging parts so they would break if anyone else tried to show them. Dr Beireis had this partly repaired, but when Goethe viewed the duck in 1805, he found, “Vaucanson’s automata were paralyzed. The duck had lost its feathers and, reduced to a skeleton, would still bravely eat its oats, but could no longer digest them.” The duck was 108 years old when Rechsteiner, a skilled mechanician, was hired to repair it. It was exhibited in Italy in 1844 and in London two years later. After that it dropped out of sight. Some photographs turned up in the early 1950s, evidently left by the former curator of the Paris Museum of Arts and Crafts. They are glass plate negatives that probably date from before 1900. The skeleton they reveal, together with the appearance of the mechanism, strongly suggests the wreckage of Vaucanson’s duck, as they were labelled. The plates were said to be from Dresden, and if the duck survived World War II, one hopes it is in a dry attic. The musicians were lost from sight sometime around 1800. None of the imitations of Vaucanson’s automata, including mekaniker Rechsteiner’s duplicate duck, now survives. These wondrous mechanisms are altogether lost.

Vaucanson himself seems to have prospered (he was a member of the Academy of Science in 1777) and continued inventing. In 1741 he devised the system of punched cards that controlled looms in the Jacquard tapestry factory. This is generally considered to be the first digital number storage and readout system. In 1760 he invented the modern metal-cutting lathe, with a shaped guideway to prevent chatter and twisting of the tool.

Mechanism of the Automata While relatively simple to explain and easy to grasp when explained, Vaucanson’s machines really are very sophisticated in performance and embody concepts easily 100 years ahead of their time. The weight-motor is a heavy weight suspended from a rope wrapped around a drum windlass, which, while slowly falling, drives a gear-train (speed controlled by a governor). These gears slowly turn a cam-drum, the master controller “memory” mechanism, one rotation of which equals one performance of the automaton. This drum, perhaps the diameter of a small keg and three feet long, has on its surface an array of rows of studs of some sort, nails or wooden knobs. Cam-followers, some sort of spring loaded levers, ride on the drum surface, one for each row (circle) of studs in the array, and each cam-follower is for a moment pushed out of place if a stud rotates by to push on it.

There are as many circles of studs on the drum as there are functions of the automaton to be controlled, and the cam-follower unique to that circle of studs does the controlling. Thus, one row, say, controls the dilation and contraction mechanism of the lips, and another row might manage the movements of the first finger, left hand, and so on. There would be about 12 functions to be controlled, so about 12 rows or circles of studs are on the drum. It is rather like a giant music box movement, except that instead of steel needles being plucked, cam-followers are displaced, and with displacement each follower pulls on a flexible cable which is linked by its own pulley system to the finger, lip, or valve that is unique to it. In some cases, like the lip control mechanism, the requirement to produce music is for smooth variation from one size to another, so the row of studs for that function is replaced by a smoothly varying curve, a cam. In other cases, the fingering mechanism, a finger either does or does not cover a flute hole. This is digital control (the word comes from counting on the fingers); the former is analog, meaning that a little movement here causes a proportional movement there.

When it is all put together and regulated carefully, the machine will play the flute using wind pressures as selected by the distributor valve. For the sake of impressive appearance, the machine is covered with a wooden framework in human shape and is clothed, but it would do its job bare. However, it would look like a machine and not a person.

The tabor and flageolet player is similar, but probably only two levels of wind were employed, and the fingering is simpler, probably four fingers.

The duck was essentially a giant version of the mechanism that operated the bird figures described earlier but with many more, and more complex, movements. While it is possible that some weight sensitive area was built into the pedestal so that the duck started to gobble the food only when a plate was placed before it, it seems much more likely that the operator carefully memorized the duck’s movements (which, of course, are identical every time) and returned with the plate at just the right moment. Otherwise the bird would have been gulping down thin air.

If they still existed, these machines would provide an intriguing catalog of early 18th century movements, probably including some that Vaucanson devised for special purposes that would not be rediscovered for 75 years or more. But, as computers, the machines were incredible. Here, 240 years ago, was a digital and analog computer preprogrammed with perhaps 300 to 500 bytes of read only memory, each byte 10 or 12 bits wide. Vaucanson appears to be the first person to have seen the need for synchronous control of multiple functions (how else could you play a flute except by regulating breath angle and pressure while simultaneously fingering the proper notes?) as well as the first who saw the possibility of designing mechanisms to effect such control. That he used the music box spindle approach to his problem is not to his discredit, for that mechanism was known to function reliably over long periods while undergoing little wear. His incorporation of music box memory devices into an array on a single drum (the master controller) enabled him to produce some remarkable results. He could control a variety of simultaneous, interdependent functions because they were all driven by the same “clock.” This was parallel data processing, in relatively small chunks, to be sure, but parallel beyond doubt. The likes of it were not seen again in mechanics until the player piano with its paper tape. It is not so very different from the way the central nervous system deals with data in many parallel channels simultaneously.

But why is this surprising? Jacques de Vaucanson was attempting to create life. It was his genius to approach the task in the manner of living things.”

3 comments
  1. Toronto says: September 8, 20119:33 pm

    I’m looking forward to part 2, even if it doesn’t have any ducks in it.

  2. Sean says: September 9, 20115:00 am

    Cracked did a good piece on this yesterday: http://www.cracked.com/…

    The video of the writers is…… something.

  3. Charlie says: September 9, 20119:38 am

    Toronto: I have part 2 scanned, I need to look and see if I have the mag with part 3.

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