Talk:Gray code

Can Baudot's use of reflected binary codes be explained, or even verified? What I find in sources don't show any Gray-like code, nor how we might have used them. Dicklyon (talk) 01:33, 19 December 2020 (UTC)Reply

I mean, I can see that if you sort his codewords in Gray-code order, the vowels come out first, in alphabetical order, then a few things and the consonants in order. Presumably there's a reason for that. But what? I can't see a relationship between how Baudot codes were used and the properties of Gray codes. And I can't find a source that mentions it. Anyone? Dicklyon (talk) 03:16, 21 December 2020 (UTC)Reply

(edit-conflict) Hi Dick, I have meanwhile added many references describing this in better details. I'm still trying to dig deeper in the history to find answers to a few of my own open questions, but regarding your question, what I found in the sources so far is that this particular arrangement was chosen to make it easier for the operator to memorize the patterns, and possibly also to make it easy to enter the chords. The synchronous Baudot telegraph used a chorded keyboard and the operator's input had to be manually kept in sync with the machine while keying in the chords, so this was very timing-sensitive.

One source also mentioned that the codes were arranged in order of frequency, but this is wrong (the later Murray code was arranged this way, but not the 5-level Baudot code).

--Matthiaspaul (talk) 23:46, 21 December 2020 (UTC)Reply

What sources say such things? My impression was that it was more about the scanning machine's teeth, nothing to do with the operator. Dicklyon (talk) 04:25, 22 December 2020 (UTC)Reply

I trimmed that section down. I couldn't find anything in sources to suggest the Mimault's telegraph used a Gray-like code and there was a bunch of text and excess refs unrelated to Gray code. Baudot and his code have their own articles. Dicklyon (talk) 23:36, 21 December 2020 (UTC)Reply

@Matthiaspaul: Could you be so kind as to explain how the material you added back helps understand how the Gray code was used? Can you explain how it was used and why it mattered? Is there a sourced explanation we can incorporate, or just the somewhat cryptic French one? Dicklyon (talk) 20:18, 22 December 2020 (UTC)Reply

@Matthiaspaul: That section on telegraphy remains cryptic and uninterpretable, and has now been bloated up with fancy tables that don't help at all. Why/how do the properties of a Gray code become relevant in that context? I'd delete the section if no relevance can be shown. Dicklyon (talk) 05:33, 29 December 2020 (UTC)Reply

Huh? The section is top relevant here per the sources because it documents the usage of what we now call Gray code or reflected binary code long before Stibitz and Gray, and even by two people independent of each other, Schäffler and Baudot (both in the telegraphy business). Schäffler's usage can be traced down to a telegraph he produced in 1874 (and Lambert claimed to have shown him this code in 1872). Baudot's usage can be traced down to a telegraph he built in 1875/1876 (many sources attribute this to his 1874 patent, but the prototype documented there still used a 6-level rather than a 5-level code). Baudot's research on this started in 1872 as well. (Mimault - at his time unsuccessfully - claimed priority on some aspects of Baudot's telegraph, including the code, so this would deserve at least being mentioned for NPOV.)

The 1872 date is relevant because it coincidentally matches the date when Gros described his "baguenodier".

The Schäffler and Baudot code tables clearly show that they actually used codes very similar to Gray's. Some of the modern sources (even top RS ones) actually call them "Gray codes".

Like you I want to find answers as to why they used these codes because this is historically interesting, but the question if this belongs here or not is already answered by the fact that they used these codes, not why.

It is relevant to describe the codes as fixed-length 5-level codes - ideally, we would avoid the term 5-bit, as some authors do, because this is long before Shannon's introduction of bits, and even the idea of binary codes was new and terminology non-established (that's why some of the historical descriptions are what you call "cryptic" - they weren't in the context of their times).

As I mentioned already, the Baudot multiplexing telegraph was still a synchronous telegraph and it used a chorded keyboard. The operator's input had to be manually kept in sync with the machine while keying in the chords, which was very timing-sensitive.

These timing constraints could have been one of the reason(s) for why the code was arranged the way it was.

What I also found in the sources is that the code was arranged to be easy to type and remember for the operator. I don't know if this was the primary goal or a by-product of the timing constraints. Either case, it certainly contributed to reducing the error rate and increasing the speed an operator was able to key in the chords while keeping in sync with the machine.

--Matthiaspaul (talk) 14:40, 30 December 2020 (UTC)Reply

I think it is wild speculation to associate the choice of a Gray-like code with the telegraph being multiplexed, or synchronous, or having a chorded keyboard. If anything, sources suggest maybe some internal scanning order of matching the inputs, which is itself unrelated to the code-letter ordering. Different tables use different codes, sometimes Gray-like and sometimes not. So I think it best to say that some sources have recognized Gray-like codes in some of Baudots machines, rather than to put all the stuff that is only speculatively related. Dicklyon (talk) 05:37, 6 January 2021 (UTC)Reply

And what is the point of the "Plan of 5-level signals" table? And what is the point of the Schäffler table that doesn't even associate the codes with letters or anything meaningful? Are they just there as pretty pictures, or is there something we can learn from them relevant to Gray codes? Dicklyon (talk) 05:42, 6 January 2021 (UTC)Reply

From the Zemanek ref, it seems clear that, in Schäffler's case at least, the reflected binary code was part of the printer's internal scanning order; there's no necessary connection from there to the ordering of characters in the printer or the assignment of codes to characters, except that they have to be consistent. This makes good sense. Saying that Baudot used reflected binary in his code makes much less sense; did he have a printer with characters in that order, and so decided to assign the codes that way? And who first observed that Baudot used a reflected binary code? I've ordered a copy of the Knuth volume that has this, but that seems to be 2005, and it came into our article in 2002, so I still wonder from where. Dicklyon (talk) 05:44, 24 January 2021 (UTC)Reply

And the Moncel ref goes into detail on Baudot's "combinateur" which lays out the symbols with Gray code, to control the scanning recognition for printing, as in Schäffler's machine. Too bad it's in French; can anyone translate the juicy bits for us? I'm pretty sure it's still just an internal detail, not related in any significant way to what codes go with what letters. More about printing than about telegraphy, really. Dicklyon (talk) 06:48, 24 January 2021 (UTC)Reply

I OCR'd, corrected, and had translated the Moncel ref. Lots of interesting details in there, including a section on the alphabet, but no clue about any Gray-code-like properties. The key bit where it could have been mentioned is here:

The characters of the type wheel do not follow each other on thiswheel in alphabetical order, but in the following order:1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16A É E I O U Y B C D F G H J ...

If you look at the codes corresponding to this order, they are the reflected-binary codes. The reason for choosing such a code is that they are laid out consecutively in that order on a wheel with 5 contacts, and they don't want more than one transition, potentially causing a glitch, in going from one position to the next as the wheel turns. Some of the other sources imply that, but this one really doesn't. I'm going to remove it.

My point is, the Gray code is not about the assignment of codes to letters. It's about the internal ordering of the characters on the printing wheel. More to do with printing than with telegraphy, and nothing to do with multiplex or with the keyboard; synchronous, yes, if one character is printed per wheel revolution and it turns at a constant speed.

Feel free to hat/hide this if you know how: Dicklyon (talk) 00:03, 25 January 2021 (UTC)Reply

Multiple transmission printing telegraph systems andelementary signal combinationsby M. Th. du MONCEL.(Continuation and end.)M. Baudot's system.We have seen by what series of combinations andreasoning Mr. Mimault had been led to his systemtelegraphic printer, who was first (in 1874) electro-chemicaland 5-wire, then electromagnetic and one-wire, by its application tothe Hughes device and its combination with the Meyer system. PointThe start of Mr. Baudot's system was different. At the time he haswas designed, there was much concern about the telegraph atmultiple transmissions from Mr. Meyer who had given excellentresults, and M. Baudot sought whether there would be no way of applyingthe principle of this system at Hughes' printing telegraph, inused for some time on the main lines of Europe.But this idea was difficult to realize, precisely because ofthe unequal spacing of the prints which could vary from 1time up to 28 times, without there being any way to regularize it,since the type wheel in this telegraph runs at aperfectly uniform way. It is certain that if by some meansmechanical we had been able to carry outimpressions after the same space of time and to ensure thatthe letter Z, for example, which is the last of the alphabet, could happenin front of the printing mechanism as fast as the letter B, we would havebeen able to devote a determined time to this function which would have beenstill the same, and the signal preparation time could havebe used for other transmissions made by other devices,as in the Meyer system. But this problem that hadpreoccupied as early as 1848 Mr. Highton, though difficult to resolve, haddid not frighten M. Baudot, because in 1872 he had combined a systemtelegraph in which functions of this kind wereobtained. He had in fact succeeded by means of such a printerfour-wheeled types, progressively advancing relative to each otherto the other, to obtain the printing in Roman characters of the differentletters transmitted according to the Morse vocabulary. In this system,current emissions corresponding to lines movedlongitudinally the wheels on their axis, so as to bring eitherone or the other of these wheels above paper, and the emissionswhich corresponded to points, rotated this axis,different quantities depending on whether one or morethe other of the wheels was above the paper.By modifying this system a little, M. Baudot was quick to make itbetter able to meet the demands of the problem it had posed, inreducing to one the wheels of the types and reacting on itsmotor axis three electromagnets which, by means of three wheelsratchet of different diameters, could turn it onegreater or lesser quantity.The action of these three electromagnets depended on a kind ofrheotome governed by two electromagnets interposed in theline circuit and reacting, one to place this or that of the threefirst electromagnets in the circuit of a fairly strong local batteryto determine the rotation of the corresponding ratchet wheel, the otherto close this circuit under the influence of an inversion of the current ofline succeeding the first programs produced. However forobtain the stop of the type wheel when passing thecharacter designated before the printing mechanism, it was necessary thatmovements of the three ratchet wheels which controlled thewalk were exact multiples of each other, and that thesemultiple were such that the combined and repeated movements ofthese wheels could make the wheel of the types take the 28 positionsnecessary for printing the different characters of the alphabet.However, this result could be obtained in a fairly simple way byarranging these wheels so that, for a single action producedby the 3 electromagnets, their movement was in the ratio ofnumbers 1, 3, 9; because by producing two successive emissions of theline current, each wheel could increase the stroke of thewheel of types from single to double, and one could obtain bycombination of these 6 movements 26 different positions of thiswheel, which could suffice for the immediate printing ofalphabetic characters. Nevertheless like movements tooextended from the wheel of current types and reversalsin unequal numbers were to cause some inconvenience, Mr.Baudot preferred to increase the number of original broadcasts of thecurrent as well as that of the electromagnets called to react on thedifferent ratchet wheels, and by bringing this number to 6, it was foundleads to arranging them in such a way as to provide movementsproportional to the numbers 1, 2, 4, 8, 16, 32, which allowed himto obtain 63 combinations without using each time more than onecurrent reversal. Still he thought to delete this one bysubjecting the rheotomes, at both stations, to a movementsynchronic. He then reduced the number of electromagnets to 5,rightly thinking that the 31 combinations they could providewere quite sufficient.At the time when M. Baudot dealt with the provision we have just cometo exhibit, that is to say in 1873, his apparatus did not yet resolvethe problem we talked about at the start. It was, likethose of MM. Highton, Mimault, Whitehouse, a telegraph atindependent impression which could not theoretically presentadvantages that because a character, to be printed, hadno need to wait for all those placed before him in orderalphabetical had passed. There was still a long way to go to the applicationfrom the multiple system to the Hughes, and moreover these movementsprogressive wheel types could result in largeimplementation difficulties. It is By seeking an intermediary lessdelicate in its functions and especially less complicated between the wheeltypes and electromagnets called to designate the signals thatM. Baudot was led to the ingenious device to which he gave the nameof combiner , and which enabled it, by making it a devicewaiting for transmitted signals, to make use of the systemstelegraphic synchronous motion printers, and to useto other transmissions the time intervals which couldexist between the formation of signals on this waiting device andtheir impression. It was in 1875 that this important invention waspatented, and it constitutes, by its very object, a verymarked between the system of M. Baudot. and those of MM. Highton,Whitehouse and Mimault who had preceded.As for the use of electro-mechanical functions on the risegeometric in the combiner in question, we have seenhow M. Baudot had been successively taken there; Butregardless of construction considerations that may haveput on the way, and without having recourse either to Pascal's triangle or tothe theory of algebraic combinations, it was enough for him to relateto the well-known 5-needle Wheatstone telegraph, to find outthan with 5 signal elements combined two to two, three to three,four to four, etc., he could get 31 likely combinationsto represent the letters of the alphabet and the most used signalsin telegraphy, and as by means of distributing apparatus placedat both ends of the line he could make reactthe currents transmitted on the electro-magnetic organs called toproviding the elementary signals, the problem of transmissiondirect all alphabetic signals to the dialer arewas thus solved in a fairly simple manner, without requiringlike the 5-wire Wheatstone telegraph.Here is now how M. Baudot realized theadvantages of this telegraphic arrangement to the point ofview of the speed of transmissions. If in a time t, we cantransmit a single signal, we can, in a double time 2t, andby the intervention of the distributor who will have enabled anew signal, transmit three different signals, two of which will beisolated and one resulting from the combination. In a triple time 3t andwith a new signal element in addition supplied by the distributor, wewill be able to transmit 3 singly and 4 in combination, in all 7.In a quadruple time 4t, the number of these different signalscan thus rise to 15, and in a fivefold time 5t, we canchoose between 31 different signals corresponding to the differentletters of the alphabet. During this time 5t, the most complicated signalcan therefore be reproduced. Now, assuming that each permutationline wire on the distributors is done at the same time asthat from one letter to another on the printer, we could prepare onthis one the printing of such letter that one would like while the wheelof the types would have carried out only the 5/28 of its revolution.However, since it takes some time to prepare a signal, itmust admit that part of the revolution of this wheel isused in this preparation, and M. Baudot paid him a quarter ofits circumference. The other three quarters therefore correspond to the 28alphabetical signals, and if we assume that this wheel of typesdoes as in the Hughes two revolutions per second, eachdistributor contacts corresponding to a type of the wheel inquestion will have a duration represented by (0 ", 5) / (28 + 9) or 0", 0135(0.0135 s), and this duration is more than sufficient, since, according toexperiments with the Hughes apparatus, it was recognized that thet necessary for the transmission of a signal on a line of 500kilometers does not exceed 0 ", 003. However, starting from this duration0 ", 0135, we find that the distributor, running synchronouslywith the wheels of the types, could perform 7 multiple transmissionsduring each revolution of these wheels1), which are transmittedmultiple could therefore cause the impression of 7letters, on 7 receivers, in half a second, i.e. 840 letters perminute or 504 dispatches of 20 words per hour. If we increased thespeed of distributors and receivers to the point of not attributingtransmissions that a duration of 0 ", 003, the output could beincreased to over a thousand dispatches per hour. These calculations, however, doshould be considered as purely theoretical, and, in thepractice, it is hardly necessary to count on a yieldnel to the number of multiple transmissions that can be established.Now in M. Baudot's apparatus this number does not exceed 5, and inadmitting that with the Hughes one can transmit a letter andhalf a turn, with the Baudot device only oneyield increase in the ratio of 5 to 1.5, i.e. a littlemore than three times. Experience has shown, moreover, thatsend 300 dispatches per hour in this way on a800 kil.1) Each letter requiring 5 successive contacts of 0 ", 0135 or onetotal duration of 0 ", 0675, each turn of the distributor carried out in 0", 5can only activate a number of receivers represented bythe ratio of 0 ", 5 to 0", 0675. Now this number is 7.407. By separating theseries of 5 contacts by an interval equivalent to one contact, or notcould only have 6 multiple transmissions.From this preamble, we see that the Baudot system, likeremain those of MM. Highton, Whitehouse, Mimault, features fourdifferent kinds of devices: manipulators, receivers,intermediate waiting devices, or combiners, and a distributorgeneral whose function is not only to putsuccessively the line in relation to each of the systemstelegraphs, but also to have a single line wire producedeffects that would determine a line of 5 threads. We are going to studysuccessively these various Organs; but, first, we mustsay that these devices are arranged for five transmissionsmultiple and that, like those of the Meyer telegraph, the differentsystems which compose them are established on the same table, 'which is arranged to allow 5 employees to beconveniently installed on its sides. For this purpose, this table carrieson each of these sides three advanced parts on which arefixed the devices specific to each transmission, and the employeesare placed in the re-entrant parts. The middle of the table isoccupied by the driving devices, the distributor and the shaft intended forprovide movement to all receivers; we can see some, figure 9,the layout for one of the receivers.Manipulator . —Each of the manipulators who is represented seen byabove, figure 8, consists of a five-key keypad or forbetter to say of a vertical board AB behind which arearticulated five Morse keys, three on the right, two on the left, whichare arranged one above the other so thatfingers of both hands can easily react to the levers thatfinish them. These keys press, on the side opposite to the lever and byvia a spring, on a common metal rod K whichkeeps them in a fixed position; they are from elsewheretrimmed on both sides of the lever, below the leveritself, of four spring forks F, F which each rubon two blades, one of which is continuous and the other cut in two, thiswhich constitutes, for each key, a quadruple switch. Thiscomplicated arrangement was adopted to ensure, asin Mr. Wheatstone's rapid telegraph, that the broadcasts ofcurrents can be positive and negative, and that those followingto programs already produced in the same direction, can befind performed under an electrical influence of less energythan those produced for the first time or those whichfollow reverse emissions. Figure 11 shows theelectrical arrangements of these switches and their connection modewith the distributor, which is shown in part developed on aflat surface to the left of the figure. But before talking about theseconnections, it is important that we say a few words in the wayhow the various devices are connected and how isarranged * the distributor itself; we will therefore have torefer to figure 9.We have already seen that in this system all the receivers are put inmovement by the same motor shaft. This tree is in hh , and itsmovement is provided by a fairly powerful clockwork mechanismwhich does not need great precision, because it is, as it iswill see later, electrically adjusted with each revolution of the motor shaft.The same is not true of a second Mplaced at the other end of the table and which sets theMachine set in D . Not only must it be regularized by meansof a vibrating blade, as in the Hughes apparatus, but thedistributor itself must still be provided with a double mechanismcorrector in order to make it work completely synchronously withthat of the corresponding station, and subject to this synchronism theoperation of the receivers it governs. To achieve this double effect,the distributor's mobile system G carries a sort of boxof gearing V which we will discuss at the moment and by means ofwhich he can have his movement suspended for a timemore or less short when it is ahead of its correspondent.On the other hand, the motor shaft hh which turns the receivers E ,crosses the axis m 'of the distributor's mobile system, so as torotate concentrically with it while maintaining movementcompletely independent. With this arrangement, we understand thatit suffices to adapt to this tree hh a ZZ ebonite disc fitted with ametal contact, so that a particular wiper is carried by themobile system G of the distributor, can react electrically to abrake adapted to the motor mechanism of the shaft, and slow down itsmovement at each turn of it, if it happens, like that by the waymust take place since this mechanism has no moderator, that thismovement tends to take more and more speed.We will study this device later, but to finish with thelinks of different. devices between them, we must add thateach receiver B is accompanied by a combiner C , and that thesecombiners are both connected to the distributors D of the twocorresponding stations and receiver mechanismsto which they correspond. This connection is purely electricalin the first case; but it is both mechanical and electricalin the second, because if the electromagnets of these combinersperform the circuit combinations that must provide thedifferent signals, a working mechanical system must beagree with the wheel of the corresponding receiver types, may,by meeting the contacts related to these combinations,determine a local electrical action capable of operatingthe printing mechanism of the receiver. We are now goingstudy in detail these different organs and we will startnaturally by distributors.Distributor . - The distributor, in M. Baudot's system, is aslightly more complicated than in the Meyer system, because it has fiveparallel rows of contacts distributed around the circumference oftwo ebonite drums D , d (fig. 9) of different diameters, and oneof these rows q4, arranged on a particular disc whosecircumference follows the surface of the drum, is likely to bemoved circularly to adjust the devices according to thelength of telegraph lines. The contacts of the first threerows g4, q5, q6, arranged on the largest drum and thefollowing disc, are distributed for each of these rows insix series having six contacts each, except the last one which has onlyfour; this is reserved for the correction which we will see latermode of action, and the other five correspond to the five systemstelegraphs intended to provide multiple transmission. Theircontacts are consequently connected, for one of the rows, to themanipulators, and for the other rows to combiners andreceptors of each of these systems; however, one of thesecontacts, the last in each series, is connected directly to the polenegative of the line stack and only plays a passive role, aswill see right away. The last two rows of contacts q1, q3, whichare fixed on the small drum d and which are nothing more than tworings divided into six equal parts, are intended to connect to theline through the distributor's trotters the contacts of thefirst row and second row, depending on whether a switch is setthe disposition of each employee arranges the line for thetransmission or reception. Figure 11 shows thedevelopment of these contacts and their mode of liaison withdifferent parts of the device.The contacts of the first row of the large drum matchin series to the five manipulators and are individually connected toeach of the keys of the corresponding manipulator; so these aretransmission contacts. Those in the second row are thereceiving contacts and correspond like the first ones, byseries, to the five combiners, while being individually connectedto the five electromagnets that are part of each of thesecombinators. Finally the contacts of the third rowstill communicate in series, both with the electromagnetsof local combiners through the receiving contacts to which theyare connected by a U-shaped slider, which presses on both rows, andwith the manipulators, by one of the switches of the keyswe will call local switch . It is through thecontacts of this third row that dispatches are printedat the start and that the combiners are brought back to their positionnormal before they are brought into play again (see Figure 11).Above the distributor which is fixed, except the part corresponding tothe first row of contacts, support the changeover springs,which are seven in number. Five correspond to the fiverows of contacts we talked about, and the sixth, which isprecisely the U-spring mentioned at the moment, precedes the others,in their walk, a distance equal to the length of one of thecontacts. These springs are attached to a VG rotating arm , fig. 9, putmoving by a hollow axis m ' depending on the mechanismclockwork regularized M and through which passes as we have seenthe end of the horizontal shaft hh which controls the movement ofreceivers. However, this movement is only communicated to this arm.via the gearbox already discussedand which is none other than a ratchet wheel V to which it is connected by astrong ratchet with several teeth. This ratchet, represented in large, in 0,figure 10, with its accessories, reacts on the opposite side on arocker fitted with an ankle c which, at each revolution of the arm Gcarrying the springs, passes over an articulated lever Ipthe end of which is terminated by an inclined plane p. This lever is engagedon an electromagnetic trigger i (figure 9), adapted to the armaturea of a particular electromagnet e, and this electromagnet is relatedwith distributor correction contacts. Now it follows from thismechanism, a constantly renewed correction that maintains themovements of the movable arms of the two distributors incorrespondence in a state of perfect synchronism. Indeed theankle position c, fig. 10, of the clutch pawl in thetwo distributors is such that when the movements areperfectly synchronized, this peg, on both devices,at the same time arrives at the beginning of the inclined plane p of the leverengaged; but precisely at this moment the trotters of thedistributors arrived at both stations on the contacts ofcorrection we talked about, and since these contacts are relatedto the corrective solenoid and, they can transmit the current tothrough it and release the engaged lever lp . Therefore the ratchetclutch can pass over the inclined plane p of this leverwithout disengaging the motor mechanism of the walkers. If aton the contrary, one of the movements is faster than the other, the contactwhich causes the corrective electromagnet to react is not carried out on the devicewalking faster than after the wise step of the pawl c on thelever engaged I p , and this then disengages this pawl which does notcan re-engage only after having crossed the inclined plane p ; itnaturally results in a small delay in the walking of the supporting armtrotters, and this delay may be enough to understand the greatestspeed with which it was animated. This action is also ensured by asecond articulated lever r , which presses on the inclined plane i? and belowwhich engages the ankle c . Since the electromagnet e is aHughes electromagnet, its armature a must be put back into position andthis function is carried out at the same time as the reconnection of themechanism, by the action of two eccentrics b and f, fig. 9, whoreact on it by means of two levers l and g, the action ofone ahead of the other a little.As the contacts related to the second row of thedistributor cannot correspond, in position, to those of thefirst row, since the effect produced cannot be achieved at the sametime of arrival and departure, and that this lack of correspondenceis more or less accentuated depending on the length of the line, it isnecessary, in order to bring these contacts to an agreement between them, to settle thereciprocal position of the two discs which carry them, and it is forthat the first, q4 is likely to move on its axis.This movement is carried out using a pinion wrench K, figure9, engaged in a window adapted to the movable disc and one of whichedges, parallel to its circumference, is provided with a smallrack.By means of this system, the trotters of the two distributors inconnections therefore pass at the same time at both stationson the corresponding contacts of each series and can, thereforeway, successively establish the junction by the line,different keys of each manipulator with the electromagnetsof the corresponding combiner. Only, as the action issuccessive, it is necessary that these electromagnetsmaintain their frame in the position made by thecurrent that has passed through them, so that this action by combining withone or more others in the combiner, can provide the signaldesired. It is for this reason that we had to usepolarized armature electromagnets.Combiner . - The combiner is composed, like the distributor,a fixed part and a moving part and in addition to a systemelectromagnetic composed of the five electromagnets of which wehave spoken, and which acts like a multiple relay systemdouble contacts. Figure 11 gives a representationtheoretical.The fixed part consists of five double metal discs withnotched circular rim, arranged in such a way that the voidpracticed in one of the ledges is almost filled with aprotruding part cut in the rim of the juxtaposed disc. Thesetwo parts of each disc are isolated from each other,such that the circumference which they form externally iscomposed of parts which may be unequal in length, but whichare isolated from each other and which alternately belong totwo different discs, capable of being electrically connectedwith different circuits. All of these double discs, however, areprovided at a point of their circumference, which is the same for all,and over an arc of about 80 degrees, with a very large notchfilled with an insulating material, which leaves the device inactive forabout a quarter of a revolution of its moving part, and it isprecisely during this time that employees prepare theirsignal to manipulators.In figure 11, we assume the rings formed by these differentdouble disc systems, developed in a straight line, and fordistinguish from each other the parts belonging to eachdisc coupled, one reached them, the ones in black, the others inWhite. As these black and white parts are, by the fact, onlyisolated contacts connected to the contacts of the armatures of the fiveelectromagnets of the electromagnetic system, wedistinguish from each other by calling black the contactsindicated in black, and white contacts not tinted. That put uswill examine how these different series ofcontacts with respect to each other.The bottom AAA ring , etc. (fig. 11), which we will designate under theNo.5. Door, as seen, 8 black contacts and 8 white contactsof the same length, except the last of white which is only halfothers. If we assume the metal part of these disks dividedinto 31 equal parts, each of the black and white contacts of thisfifth ring would correspond to 2 divisions, except the last of thewhites who would only understand one. The fourth ring does not carry4 black contacts and 5 white contacts which each correspond to4 divisions, except the last two which are white and do not includethat one and two divisions. They are placed in relation to thecontacts of the fifth ring, so that the contactsblack start and end in the middle of each of the black contactsof this fifth ring. The third ring carries only twoblack contacts and three white contacts, and these black contacts, likepreviously, are arranged to start and end atmiddle of two consecutive black contacts of the fourth ring, thiswhich causes that the two white contacts which are at the endsinclude only 3 and 4 divisions, while the others ininclude 8. The second ring has only one black contact leftand two white contacts which include the first 16 divisions, theseconds 8 and 7 divisions, and always commits the black contactand ends in the middle of the two black contacts of the third ring. Finallythe first ring has only a black contact and a white contact, thethe first comprising 16 visions, the last 15. The black contactthen begins at one end of the indentation and ends atmiddle of the contact of the same type of the second ring.If we carefully consider the reciprocal arrangement of these variouscontacts, it is immediately recognized that, thanks to this arrangement,five springs R1 R2 R3 R4 R5 placed in a straight line and whichwould revolve around these 5 rings, can never meetat the same time two separations of black and white contacts, and bytherefore the functions of each of them are clearlydetermined to complement the closures of the local circuit atthrough the printing mechanism. The various black and white contactsof these rings are also connected by wires to the doublecontacts A, B, C, D, E of the 5 electromagnets of the combiner which it haspreviously discussed and which constitute what wecall the electro-magnetic rheotome. This binding is made ofsuch that the white contacts correspond to the contactsunder which the reinforcement rests in normal times, andthat the black contacts correspond to the upper contacts onwhich support these frames when they are deflected. Inexamining the position of this or that of the reinforcements a, &, c, d, e oncan easily, according to this explanation, find the open waysthrough the combiner.The electro-magnetic system is moreover nothing more than fiveSiemens polarized electromagnets, whose armature oscillates betweentwo stops forming the previous contacts A, B, C, D, E, andfound maintained in the last position it occupied, byresult of its polarity and the remanent magnetism of the electromagnet.These reinforcements being the switching members intended to put inaction the printing mechanism, are naturally related to thismechanism and the local battery P, the circuit of which must be completed bythe combiner; but as they can act more or lesslarge number, they must, with the different rings of thecombiner, be an integral part of a continuous circuit closed by themobile system of the combiner and, therefore, be linked betweenboth of them, except the one that communicates directly to thepile P. It is for this reason that reinforcements b and c , d and e aremetallically united as seen in the figure.The mobile part of the combiner is composed, like that of thedistributor, of a series of 5 spring trotters R1, R2, R3, R4, R5,suitable for an arm mounted on the axle of the type wheel and which turnswith it, and like the 31 characters on this wheelcorrespond exactly to the 31 divisions according to which wereestablished the contacts of the combiner, these springs passsuccessively before these different divisions at the same time asthe different characters of the type wheel pass in front of theprinting mechanism. Consequently, if the type wheel issuitably placed in relation to this trotter system, we canensure that by the time this system reaches the tenth or thefifteenth division of the combiner, for example, the tenth or thefifteenth letter is placed in position to be printed.The mobile system of the combiner being the counterpart of the systemelectro-magnetic and having to complete the circuit whose path isprepared by this last system, must have its trotters connected two totwo, like the armatures of electromagnets; only thisconnection must be made in an opposite way, so that the currenttransmitted circulates meandering through the five rings of thecombiner. Also it is the springs R4 and R3, R2 and R1 which areconnected together, and it is the fifth Rs that communicates with thebattery P via the printing electromagnet I.With this arrangement, it is easy to see how the current of thepile P is closed at each turn of the trotters and according to the actiondetermined on one or another of the electromagnets. Indeed, supposethat the lower keys of the corresponding manipulator havedeflects, through the distributors, the reinforcements e and cof the combiner: the current leaving the battery P will be directed bythe armature which has not moved on the white contacts of the fifthring of the combiner, and as to get out it must pass through awhite contact of the fourth ring, a black contact of the third, awhite contact of the second and a black contact of the first, it cannot befind in these conditions that when the trotters will have arrived atthe twenty-fourth division; then the circuit crossed will be as follows:armature a , 6th white contact of the 5th ring, res out R1, spring R2,4D white contact of 4th ring, armature b, armature c deflected, 2ndblack contact of 3rd ring, spring R3, spring R4, 2nd white contactof the second ring, armature of the armature deviated, black contact of thefirst ring, R5 spring, printing electromagnet, battery. Theprinting mechanism then being brought into play, prints the letter in thismoment at hand, and this letter is the twenty-fourth of the wheel oftypes. We will see later that this letter is the S.We now understand, from the functions that we come fromto analyze, which will be possible by the different combination ofpositions of the electromagnetic rheostome armatures,combination carried out under the influence of the manipulators and bythrough the distributors, not to obtain the closure of the currentlocal printer that at the very moment when the letter of thetypes, designated by this combination, arrives in front of the mechanismprinter.M. Baudot imagined still other simpler combinators intheir construction which have the advantage of being able to operatemechanically the printing mechanism, and consequently withoutlocal current. In these combiners, the fixed part of the device ismobile, and reciprocally the mobile part constituted by the springswalkers is fixed. These springs are in fact replaced byspecies of articulated rockers which carry fixed normally closeof their axis of the arms pressing on a lever depending on the systemfirst impression. Five Hughes electromagnets, in connection with thedistributor, are placed in front of one of the ends of these rockersso that their frame, when detached, can tilt them andconsequently release their arm from the printing lever. Abovethe opposite end of these rockers, is the mechanismcombinator proper which is arranged much like the onethat we have studied previously, but which, instead of contactsdifferent in nature, has alternately hollow parts andprotruding arranged, moreover, like these contacts. This cylinder,as we said at the beginning, turns with the wheel oftypes of the printer, and, in this movement, provokesnaturally the lowering of the rockers that the protruding partsmeet; so that when the turn of this cylinder has beenaccomplished, all these rockers had to be lowered, eithermechanically by the combiner, or electrically by theelectromagnets. Then the printing mechanism is released and canproduce the impression, but this impression can be done more orsooner depending on the position and number of lowered scaleselectrically, because the combiner only completes the action thusproduced, and this complement is only carried out when theposition of this combiner corresponds to the arrival of the lettertransmitted in front of the printing mechanism. This one is loadedthen, after printing the letter, take care to re-enter allthe scales and put all the reinforcements back at the same timedeviated from the electromagnets in contact with them.This system, as is easily understood, could still beelectrically combined. It would suffice for this to keep at 5combinator electromagnets the arrangement we havestudied in the first place, and to consider the rockers from which it comesto be a question of scull switches oscillating between twocontacts and with an idle contact. By connecting these double contactsto those of electromagnets, and by metallicflip-flops two by two in an inverse manner to that of the reinforcementsof these, one of the switch systems can serve ascomplement to the other, and the combinator cylinder by carrying outrequired this complement, determines the impression by launching thelocal current through the printing electromagnet. We win at thissystem the elimination of the 5 trotter springs, and the construction ofCombiner cylinder is much simpler, since there is no longer anyisolated contacts or double discs. M. Baudot now givespreference for these two systems; but as it is the first whohas been executed so far, we had to stop there longer.Receiver . - The receptors in this system look likemuch to the part of the Hughes Telegraph which constitutes theprinting mechanism; a type T wheel, figures 9 and 12, whosecharacters occupy only three quarters of the circumference; aprinting wheel 0 provided with 32 pointed teeth in the part of itscircumference corresponding to the types of the preceding wheel and whichis mounted on the same axle of this wheel; a mechanism forpermutation of numbers and letters; a printing system I, J, x, xput into action under the influence of a triggerelectromagnetic; such are the various parts which compose it.This printing system, however, does not work as inthe Hughes apparatus; the axis with the four cams not being there,printing is done under the influence of the motor which sets in motionthe types wheel and combiner, and through the wheelof 32 teeth 0 which was discussed previously. This indeed hasfor function, when the J armature of the electromagnet isdetached, to lead an arm Ha; fixed on the articulation axis of thisframe, which is currently within reach of its teeth; andas this one is equipped with a system of rollers NH ## on whichthe paper strip is rolled up, this strip can be pressedagainst the T-type wheel. This roller system consists of theremainder of two small guide cylinders xx around which thestrip of paper, and an NH rolling mill system, one of thecylinders, mounted on the axis of the frame itself, carries the snapPP 'intended to advance the paper. It's easy to understand,moreover, that the wheel of 32 teeth O which thus governs the impressioncan, being provided with a permutation mechanism similar to that whichis suitable for the correcting wheel of Hughes devices, determineprinting letters or numbers when the arm H x ; wearing therollers meet, between the teeth of this wheel, the appendixsystem which activates this mechanism.To obtain that after each printing the reinforcement ofthe electromagnet is mechanically replaced in contact with itspoles, Mr. Baudot establishes on the support of the mechanism a rocker withspring L which, being met by a peg I adapted to the wheel32 teeth O, can be tilted far enough back when passing throughthe indented part of this wheel, to make the arm travelimpression H #, in the opposite direction of its first movement, the arccircle he had described under the influence of the triggerelectro-magnetic and the drive produced by the O wheel.The result is that the armature J is again brought into contact withthe electromagnet I, and therefore able to providenew action.Linking devices to each other. - Now that we have describedthe way in which the organs of the manipulators of thedistributors, combiners and receivers, we willto be able to study more easily their mode of connection, and welet's start with the manipulators first.We have seen that these devices were each equipped with fourswitches having the form shown, fig. 13, where only twoare figured. These switches each consist of a springinverted U rubbing on three contacts, one which is long and whichcorresponds more or less directly to the distributor's contacts,the other two which are short and which also correspond moreor less directly to both poles of the line stack. In fig.11, which represents all the connections of the devices, these fourswitches are indicated only by their contacts, and it is necessaryto admit consequently that there exist above them the trotters inU of which we have just spoken, which bring together in long contact,depending on whether the button is raised or lowered, the upper contactor the bottom contact. In this figure, only theswitches related to three of the keys of a manipulator,the connections being always the same for the other keys. Over theresame reason, only part of the distributor's contacts have been shown,and these contacts are shown on the left at the top of thefigure. The trotter springs of this distributor are indicated in r, r1r2, r3, r4, and the direction of their movement as well as that of the springsR1, R2, R3, R4, R5 of the combiner is indicated by arrows. The+ and - signs indicate that the contacts to which they belongare placed in direct contact with the two poles of the line stack, andthese same signs surmounted by the letter R indicate that aresistance has been introduced through the communication wires of thisbattery to reduce the voltage.From the inspection of the figure, we first see that the firstswitches of each key are set by their long contacts inreport with the plates of the local distributor, and only receive thecurrent, except that of the first key, only through thesecond and third switches of the preceding key, whichcommunicate to it, depending on whether the transmissions are made withcurrents succeeding each other in the same direction or in opposite directions,more or less strong electric charges. It is precisely thesevariable loads that keep the line at the samepotential and realize the benefits Mr. Wheatstone has achievedin his fast telegraph with the compensating currents.Let us indeed follow the course of the currents in a transmission madeusing keys 3 and 4 down. Unweakened positive current will befirst directed to the third distributor contact; because the line isalready under the influence of a negative charge that it still hasin normal times, and this current transmitted by the third keycomes through the third switch of the secondkey not lowered. Immediately afterwards, a new positive current issent to the distributor's fourth contact by the fourth keylowered but it is weakened, because it does not reach the firstswitch of this key only through the thirdswitch of the third key which is then lowered and whosesecond contact is related to the weakened pole of the battery. Asby the time this current crosses the line, it is already loadedpositively, it therefore only needs a weak positive charge totake back the potential it must have to functionregularly. If instead of lowering keys 3 and 4, we had loweredkeys 2 and 4, it would not have been the same: a first currentpositive non-weakened would have been transmitted by the second touch to thesecond distributor contact in the same way as thatpreviously transmitted by the third key, but the one that would havetransmitted the fourth touch would not have been weakened, because the thirdkey not having been lowered, the current would have arrived at the firstswitch of the fourth key by the first contact of thethird switch of the third key, and this current notweakened would have been essential to reverse the loadweakened negative that the line would have acquired under the influence of thisthird key not lowered.It remains for us to discuss the functions of the fourth switch ofeach key, functions that are double, because this switch is usedboth for local impressions and recall to their positionnormal of the electromagnetic armatures of the combiner. Asfor the others, the two contacts of this switch are connected to thetwo poles of a battery; but this stack is a local stack, and eachlong contacts of these switches is connected to a contact of thethird row of distributor. Normally, this long contactbeing connected to that of the switch contacts related to thenegative pole of the local battery, it happens that when the manipulator does notnot working, all the contacts of the third row of thedistributor are negatively charged, and therefore when thesmall spring, in U of the distributor (the one that precedes the others) comes topass over these contacts, it successively transmits this load to thereceiving contacts who, transmitting it in turn toelectromagnets of the local combiner, through them determine theclosure of five negative currents. Now these negative currentsthen recall to their normal position those of the reinforcements of theseelectromagnets which would have been deflected in the previous turn of thedistributor, and as the action of the U-shaped trotter precedes that of theother wipers, the combiner is placed in position to providenew combinations before the passage of these. Of aon the other hand, and for the same reason, when the manipulator is put ingame, the distributor contacts in relation to the keyslowered are positively charged and operate theelectromagnets of the same local combiner, which therefore determinesprinting of the dispatch at the outgoing post and before it istransmitted to the receiving station. Under these conditions, only oneswitch may be sufficient, because the circuit, being local, is not subjected toeffects of load variations which influence both transmissionsacross the lines.Alphabetical system . - Figure 14 below shows thealphabetical system adopted by M. Baudot. The different signalsthat can be done with the right and left keys areindicated by small circles placed in squares, and these signalsbeing arranged like the numbers to be combined in a table ofmultiplication, we can see, by following the leagues horizontally andvertically, what is the letter designated by each combinationsignals. This table is double to match the twowheel positions of types which provide printing of lettersand that of numbers. This is how we see that the lettercorresponding to a simple lowering of key N ° 1 of theright manipulator is' A, that lowering the firstright key and the first key on the left give theJ, that the three keys on the right and the two keys on the leftlowered give the P, that the isolated lowering of the two keys ofleft gives the white letters or the numbers, etc. Wemust however note that the order of the keys on thesetables must be interpreted, in relation to that indicated on thefig. 11, as if the two keys on the left represented thekeys 1 and 2, and as if the three keys on the right representkeys 5, 4 and 3, keys 2 and 5 being indicated plotswhich correspond to indexes. If we follow on the combiner thenumbers of the divisions to which the variouscombinations indicated in these tables, it is recognized that the lettersthat they designate do not correspond to their rank in the orderalphabetical. This is due to what M. Baudot wanted, as inthe Morse alphabet, apply the simplest combinations tomost frequently repeated letters in dispatches. Thecharacters of the type wheel do not follow each other on thiswheel in alphabetical order, but in the following order:1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16A É EIOUYBCDFGHJ White numbers17 18 19 20 21 22 23 24 25 26 27 28 29 30 31KLMNPQRSTVWXZ t Blac lettersOperation of devices . - Now it's time to seehow all these devices work, and we'll assume thatit is the third manipulator of station A which is put inaction to transmit the letter H to station B. The employee ofstation A will then lower the first two buttons of theright manipulator and the second from the left manipulator.Depending on the arrangement of the devices, these lowered keys will bethose we have designated in fig. 11 under the numbers 2,4, 5. This reduction will be carried out during the passage of the resortswalkers in front of the insulating part of the distributors that wesuppose to walk synchronously. When these springswill reach the third series of contacts of these distributors, theline will be put in contact, by contacts N ° 2 of this one with thereinforced positive pole stinks a line and that by key N ° 2. Thepositive current arriving through the second contact of the distributor of thestation B to the second electromagnet of the third combiner, willtilt its armature d on the contact in relation to the black contactof the second ring of the combiner. Almost at the same time thekeys 4 and 5 of the manipulator will transmit through contacts 4 and 5distributors of equally positive currents that will cross theelectromagnets 4 and 5, and will bear their armatures a and b on thecontacts corresponding to the black contacts of rings 4 and 5 of thecombiner. However, the positive charges thus transmitted do notwill not be the same, because button 3 is not lowered, thepositive charge which will be transmitted to button 4 will be reinforced,while it will be weakened for key 5 due tolowering of button 4 which preceded it. So we will find ourselvesin the case of good transmission, and the three reinforcements a , b , ddeviated will open to the local current, when the trotters of thecombinator will come to pass, the following way: deflected armature a ,fourth black contact of the fifth ring of the combiner, springR1, spring R2, second black contact of the fourth ring,deflected armature b , armature c , second white contact of the thirdring, spring R3, spring R4, black contact of the second ring,deflected armature d , armature e , white contact of the first ring,spring R5, battery. But that will only be when the trotters arearrived in front of the thirteenth division that this current will be completed. Goldthis thirteenth division corresponds precisely to the letter H.It is easy to understand that the same effects being reproduced onelectromagnets of the local combiner of station A which transmits, theletter H will be found in the same way printed under the influence offourth switch of the three down keys.Ultimately, we see that, by this system, all letters ofthe alphabet and numbers can be printed under the influence offive keys that are held constantly under the fingers,and that we lower in such or such order as is appropriate to represent the 31 letters and signs of the alphabet. Without doubt thisimpression is not made instantly at the time oftransmission, but the time separating successive impressionsis regularized, and can be used for other transmissions, whichare carried out successively in the same order and whichquintuple the number of dispatches sent and received.This device was built with great skill by Mr.Dumoulin-Froment, the son-in-law and successor of the illustrious builderM. Froment, and as I have already said, the first tests were verysatisfactory. It is hoped that this system can beadvantageously applied in practice.Postscript . —As a result of an error by the copyist certain sentencesfrom the previous article that had been erased in pencil on mymanuscript, have been reproduced and suggest that the firstM. Mimault's system was likely to apply to themultiple transmission; but as we could see by the last oneparagraph of this article and the preliminary account of the system, it does notis not so. This system could have no other result thanto print directly and independently of each other thedifferent alphabetic characters, as did the restMr. Highton's device. Multiple transmission did not havemoreover its raison d'être, under these conditions, since there was thenno time wasted in transmissions.

Rothen, Timotheus (1878-12-25). "La télégraphie et quelques autres applications de l'électricité à l'Exposition universelle de 1878: Appareils duplex, quadruplex et multiplex". Journal Télégraphique. La télégraphie et quelques autres applications de l'électricité à l'Exposition universelle de 1878 (in French). IV / #10 (12). Berne, Switzerland: Le Bureau International des Administrations Télégraphiques: 247–254 [252–254]. eISSN 2725-738X. ISSN 2223-1420. ark:/12148/bpt6k5661719x. Archived from the original on 2020-12-19. Retrieved 2020-12-19.

If we look at the pI disc, we find in divisions 2 to 5, 10 to 15, 22 to 25 and 30, in all four notches, in the pII disc 7, in the pIII disc 9, in the pIV disc 10 and in the pV 8 disc, for a total of 38 notches. […] By notching the discs according to the drawing in figure a, we would have obtained 38 jolts for the disc levers, during a single rotation of the latter. The regular functioning of the apparatus would perhaps not have been hampered by these 38 jolts, but, in any case, they would not have been favorable to its functioning, since the levers of the discs are intended to establish the contacts. of the local current of the printer relay. […] M. Schäffler was therefore led to seek a more advantageous solution in the displacement of the notches, so as to obtain a more suitable series of divisions. […] He solved this problem by empire. […] Figure b was formed using 31 small pieces of wood, which could be moved at will. Wood No 1 was set aside, Mr. Schäffler using only 30 permutations. […] He moved the antlers until he came to figure b. This is how we find wood 8 next to wood 21 and so on. This arrangement was the most favorable and the notches of the discs followed each other in such a way that the lever of the disc pI fell once, pII 1 time, pIII 2 times, pIV 4 times and pV 7 times, in all, all the 5 levers 15 times, in a notch, instead of 38 times as in the first arrangement. […] The only purpose of this arrangement is therefore to free Mr. Schäffler's device from a few drawbacks. [...] If now M. Baudot's model resembles M. Schäffler's permutation disks, we can simply conclude that M. Baudot enjoyed the same advantages as M. Schäffler. […] However, the two systems cannot be absolutely equal because Mr. Baudot uses 31 permutations, while Mr. Schäffler is satisfied with 30. […] In general, the two devices are only alike in idea apply the multiplex system to printing devices. 

The "notch" I presume is between positive and negative contact regions on the disc, corresponding to bit transitions between codes. Minimizing them is good, and is equivalent to having only one bit transition per code transition. But this guy misses the point. It's not about minimizing the number of jolts but about avoiding the possibility of glitching, when the printing wheel scans for a match to the character code. He got this close to being able to say something about the reflected binary code and it's raison d'être, but flubbed it. I already removed this ref from the article, since it has nothing relevant to Gray code.

Let's look at how the article's comments on Baudot got to where they are.

• In this 2002 edit, we got "The French engineer Émile Baudot used Gray codes in telegraphy in 1878. He received the French Legion of Honor medal for his work.", unsourced, from User:Heron. I presume he got that from a source, but don't know what.
• In June 2014, at Talk:Gray_code/Archive_1#Baudot code, one of the first use of Gray code, an IP proposed saying more about Baudot.
• On July 3, 2014, the IP added a ref to Pickover's Math Book, of 2009, which says "The French engineer Émile Baudot used Gray codes in telegraphy in 1878", quoting our article without attribution. And it has a direct copy, plus color, of the patent drawing that I upload in 2006. Seems like clear WP:CITOGENESIS to me.
• On July 4, 2014, User:Glrx pushed back on the talk discussion and asked for a reliable source, but didn't do anything about the article.
• That's where it sat until December 17, 2020, User:Matthiaspaul started adding a whole bunch of refs about Baudot, most not saying anything in support of him using a Gray code, as far as I can find.

What we really need are secondary sources that connect these telegraphy bits to Gray codes. I see Knuth does that, so I'm getting a copy to inspect in depth. Dicklyon (talk) 03:01, 24 January 2021 (UTC)Reply

Based on discussion above, and more studying of sources, I've pared it back again. It's clear that both Baudot and Schäffler had discovered and used the essential properties of Gray codes in their printing mechanisms, so it's best to focus on sources that say something about that. Multiplexing and keyboard differences are irrelevant, and assignment of codes to letters nearly so. Dicklyon (talk) 00:40, 25 January 2021 (UTC)Reply

I needn't have waited for the Knuth book, as I see I had found it before and linked it above (here). It says "More significantly, Γ5 was used in a telegraph machine demonstrated in 1878 by Émile Baudot, after whom the term 'baud' was later named. At about the same time, a similar but less systematic code for telegraphy was independently devised by Otto Schäffler." That about it: "used in a telegraph machine" is supported by the sources, but the Gray code is still not very relevant to the Baudot code, or Schäffler's code, itself. It's an internal detail of the sequential character matching at the print wheel. Not sure why he says "code for telegraphy" in Schäffler's case. Dicklyon (talk) 00:07, 3 February 2021 (UTC)Reply

An IP editor claims the expressions are different from what's given in the ref. ~Kvng (talk) 13:18, 25 May 2021 (UTC)Reply

The number of transition in each dimension is necessarily even. The IP's claim look therefore plausible, while the current claim in the Wikipedia article must be wrong. --FvdP (talk) 15:42, 17 December 2021 (UTC)Reply

I'm not sure why the table of values at the very top of the article also includes a different coding scheme which is not explained anywhere else nor has an article of its own. It makes the table more difficult to read while not adding anything that's related to the article, I suggest it's best removed Ruse.mp (talk) 07:58, 29 December 2022 (UTC)Reply