Philosophical Society of Birmingham
III Babbage's Calculating Machine.
By WILLIAM P. MARSHALL, M.I.C.E.
[Read before the Society, December 18th, 1873]
This celebrated machine, which was ten years in course of construction, at government expense, from 1828 to 1833, at a cost of £17,000, has excited great interest and is by far the most advanced calculating machine ever designed. It was designed and constructed by the late Charles Babbage, who is only recently dead (in 1871), and the subject occupied a great many years of his life. The machine that now exists, although complete in itself, is really only a portion, and a very small portion of his entire design; but the remainder, though much was done in the construction of the machinery, has never been completed, nor any other portion been put together. The progress of the work was suspended for nine years, (1833 to 1842) in consequence of the want of a further supply of government fundu, and the whole was then finally abandoned after as much as £17,000 had been expended upon the construction of the machinery.
The present machine has now remained thirty-five years locked up in a glass case and practically inaccessible until it was brought out at the recent International Exhibition of Scientific Apparatus at South Kensington, and was there shown, and occasionally at work. It continues at South Kensington in the Educational Department.
An elementary diagram of the machine is given in Figs. 1 and 2, Plate 2, showing the, leading parts, for explanation of the general construction and action of' 'the machine. The first appearance of the machine itself gives the impression of a bewildering complexity in construction and working; but upon looking into it the whole is seen to be built up essentially of a series of repetitions of certain pieces of apparatus arranged symmetrically. The principle of the machine is indeed based entirely upon the idea of subdividing an operation that is in itself very complex, into a number of separate individual movements, that each one becomes manageable by simple mechanism. The great difficulty in designing the machine was so to combine and arrange these numerous movements that they would correctly and precisely follow one another, and unite in producing the intended combined effect without any interference with one another ; —and the difficulty became so excessively great of following each movement in the design of the machine through all the subsequent superimposed movements, and tracing out the final resultant effects, that Babbage had to design for the purpose a new and remarkably ingenious system of mechanical notation and graphic representation of the several movements in combination, before he could proceed to work out his design.
The object that he had in view in this calculating machine was to obtain the means of calculating with absolute accuracy the tables of figures (such as powers of numbers, logarithms, &c.), that are required for nautical, astronomical, and other important purposes. In these tables their whole value depends on the absolute accuracy of every individual figure, as any one of the figures in table may become involved in some important calculation ; but from the multitude of figures employed in each calculation the difficulty becomes extremely great of obtaining this accuracy by hand-work (or rather head-work), and Babbage desired to substitute machinery that would be totally independent in its detailed working of any human and consequently fallible influence.
Anyone adding up long columns of figures finds how difficult it is to prevent some accidental error creeping in, although that operation consists only of' a repetition of the simplest process of arithmetic but this difficulty becomes far greater in the complex calculations referred to, and the risk of error is much greater than would at first be supposed, even with the most practised calculators. A remarkable illustration of this occurred in the case of the calculation of a Catalogue of Stars by the Astronomical Society, as related by Baily, former Astronomer Royal. The computations were done by two separate and independent persons, and then checked by a third skilled calculator, and finally submitted to Mr. Baily himself for examination ; and then from some discordance that he observed he had reason to suspect an error in the calculated position of one of the stars, amid consequently re-calculated the position, when in the first instance he obtained precisely the same result as before; but not feeling satisfied he went over the calculation a second time, and then found it was really wrong, by accidentally discovering that they had all inadvertantly fallen into the same error in the calculation.
Another striking instance of errors escaping detection was in a much used Table of Logarithms called "Taylor's Logarithms," published at time end of the last century (1792), in which forty years afterwards (in 1832) some errors were detected from a comparison with a set of unpublished tables that had been calculated in France; and a careful examination led to the detection of 19 errors, which were consequently published as a list of errata in the "Nautical Almanac," the tables themselves being in use for calculating the position of ships at sea. But in the, next year's Almanac, an erratum of one of these errata had to be published, and in the following year there was actually a second erratum required of this erratum. It is a remarkable fact that of the above-named 19 errors, 18 were simply errors in carrying, 11 of them being omissions to carry 10, and 7 cases of carrying 10 when there should have been nothing carried. The 19th was a printer's error, inverting a type of 9 and making it into 6. It has been stated that in 40 different tables taken by chance, including tables of powers of numbers, multiplication tables, and logarithms, the number of acknowledged errors published in lists of errata amounted to no less than 3700 altogether.
This difficulty of ensuring absolute accuracy vanishes, however, directly the process of calculation can be reduced to the movements of machinery, because machinery is not able to anything but repeat its own movements precisely, having no power of will or possibility, of involuntary action. The accuracy of results is then; of course dependent upon the correctness of construction of the machinery, but that is a point that can be definitely ascertained once and for all by inspection before the commencement of working; to avoid for instance, any such defect as an error in the number of teeth in one of the wheels, such as has been a cause of recent complaint in some gas meters, in which an error in the number of teeth in one wheel of the counting gear caused the meter to register falsely. A deficiency of one tooth for instance, in a wheel of 50 teeth, would cause an error of 1 in 50, or 2 in 100, that is 2 per cent. overcharge in the register and in the consequent charge for gas.
Another essential point in machinery is that it is thoroughly firm and substantial in construction, and free from any risk of slipping or springing, so as to cause a false movement; and in Babbage's machine this is admirably provided for by all the parts being made so strong, and the wearing and rubbing parts so hard and well formed, that they cannot do otherwise than act correctly.
As a very elementary illustration of a calculating or counting machine the dial of a watch may be mentioned, in which the minute-hand counts the number of revolutions of the second-hand, and the hour-hand counts the number of revolutions of the minute-hand. A step in advance is the counter of a gas-meter, in which the counting is effected by a series of separate dials connected decimally and counting hundreds, thousands, &c., of revolutions of the gas-meter drum. These two cases have the defect, however, that the dial hands are always In motion, creeping gradually on from one figure to the next, and only standing pointing definitely to any figure when the next dial behind happens to be at 0. In Babbage's machine, however, all uncertainty in reading is avoided by the dials standing quite still when read, and when they are in motion each one moves suddenly and precisely from one figure to the next.
The principle on which the machine acts in calculating tables is that of adding continuously a constant difference being added to the previous number at each successive complete movement of the machine, so as to form a new number; and the true name of the machine that exists is consequently "The Difference Engine," which was the term applied to it by Babbage himself. The simplest illustration of this principle is in the calculation of a table of squares. Taking the series of Natural Numbers, 1, 2, 3, 4, 5, &c., as shown in the following table, their several squares are 1, 4, 9, 16, 25, &c.., and the successive differences of these numbers are 3, 5, 7, 9, which are called the 1st Differences; and the difference of those again, which is called the 2nd Difference, is 2 constant.. Consequently by reversing the process, and simply adding every time the constant 2nd Difference 2 (beginning with 1 as the square of 1), the series, 3, 5, 7, 9, &c., forming the 1st Differences is obtained, and by adding these successively the required table of squares, 1, 4, 9,16, 25, &c., is obtained.
TABLE
OF SQUARES.
The same process applies to a Table of Cubes, or 3rd powers, only a 3rd Difference has then to be taken before a constant difference is arrived at, this constant difference being 6, as shown in the following table.
TABLE OF CUBES.
So also with a Table of 4th Powers a 4th Difference has to be taken for obtaining a constant difference, which is 24 ; and for a Table of 5th Powers a 5th Difference has to be taken, which is a constant of 120.
Taking the simplest of these cases, namely the calculation of a Table of Squares, the mode of action of the machine is as follows: in the front, of the machine is a series of figure-dials arranged in three vertical columns as shown at A,B,C, in Fig. 1, Plate 2, all the dials being exactly alike, and each one is marked round the circumference with a series of numbers from 0 to 9 ; the dials are placed edgeways (instead of flatways as a watch-dial) and are numbered round the edge, so that only one number at a time is shown in front of each dial, making it clear and definite for reading.
The right-hand column of dials A shows the final Squares that result from the working of the machine (omitting te bottom dial), and these are indicated by the figures shown in front of the dials, reckoning upwards from the lowest, as units, tens, hundreds, &c. The 1st column to the left, B, gives the 1st Differences, and the 2nd column to the left, C, gives the 2nd Difference. The upper three dials, D of this column, are independent of the 2nd Difference dials below, and serve to show the series of Natural Numbers of which the figures in the right hand column A are the Squares, and they are similarly arranged in order as units, tens, and hundreds, reckoning from below upwards.
The addition of the several colmnns is effected by the movement of the handle at the top of the machine, shown at E, in Fig. 1, and in the plan, Fig. 2. This handle makes a half revolution only, from front to hack and then from back to front, and two of these double strokes (two backward and two forward) are employed for each operation of producing or calculating a number for the table; the process beiug exactly the same and just as quick in performance whether the final number calculated consists of a single figure only or of several figures. This process of adding is divided into two steps, because whilst any one column is being added to the following one, this following column that is being added to must stand still ; and consequently the columns have to be worked in two alternate sets; one double stroke of the handle acting upon alternate columns, whilst the intermediate columns stand still, and wait to be acted upon by the succeeding double-stroke of the handle.
In the present machine there are only three columns to be acted upon, but the same two double strokes of the handle are sufficient for a machine with any number of columns, as all that is required being that every alternate column is standing still at any one time, and the simple rule to be followed is that the first of the two double strokes of the handle adds all the even colums to the odd ones and the second double stroke adds all the odd ones to the even ones.
The machine is adjusted for calculating the Table of Squares by setting all the dials of the Result column A at 0, those of the 1st Difference column B at 1 for the bottom dial, and the rest, at 0, and the 2nd Difference column C is set at the constant difference 2 on the bottom dial the rest being at 0 ; the Natural-number dials D are also all set at 0. The effect of the 1st double stroke of the handle (as shown in the 1st diagram of Plate 1) is to add the 1 of the 1st Difference column to the 0 of Result column, making a total of 1 as the 1st square; and the 2nd double stroke as shown in the lower diagram adds the 2nd Difference 2 to the 1st Difference column, making the 1st Difference 3, and at the same time the Natural-number dial is advanced from 0 to 1, showing the Natural-number 1 of which the Result-number 1 is the square. The Natural-number dial is advanced one figure for each two double-strokes of the handle, being each time that a calculation is completed; and at the same time the top centre dial F (which is independent of the rest and makes one entire revolution for each two double-strokes of the handle), presents in front the words "Calculation Complete," which are engraved upon one side of the dial, and this serves to indicate definitely the time where the figures in the Result column are ready to be recorded.
The next similar operation (as shown in the diagram of 2nd Calculation), adds the altered 1st Difference 3 to the result figure 1, making 4 as the square of 2; and this figure 2 is then shown by the Natural-number dial being advanced from 1 to 2, and at the same time the constant 2nd Difference 2 is added to the 1st Difference figure 3 making that 5. The next (shown in the diagram of 3rd Calculation), similarly adds this altered 1st Difference 5 to the previous Result figure 4 making it 9, which is the square of 3; the Natural-number dial being altered to 3 and the 1st Difference increased to 7, which is the required number for adding to 9 to make 16 in the succeeding operation as the square of 4.
The lower set of diagrams on Plate I show the corresponding operations for the calculation of a Table of Cubes. The machine is adjusted for the calculation in a similar manner to the adjustment for calculating Squares, by setting all the dials of the Result column at 0, those of the 1st Difference column at 1 for the bottom dial and the rest at 0, the 2nd Difference column all at 0, and the dial of the 3rd Difference column at the Constant Difference 6. There is only one dial for the 3rd Difference column in the present machine, and this is situated at G., Fig. 1, below the column of 2nd Differences, but this arrangement is only for the purpose of obtaining compactness in the machine, and the action is the same as if this 3rd Difference dial was situated at G in its natural position, to the left of the 2nd Difference column C. It is shown in this latter position in the diagrams in Plate 1, for greater clearness of explanation. In the 1st Calculation 1 is added from the 1st Difference column to the Result column, giving 1 as the Cube, and 1 is given as the corresponding Natural-number, whilst the constant 3rd Difference is added successively to the 2nd and 1st Difference columns, making them 6 and 7 respectively. In the 2nd Calculation the altered 2nd Difference 7 is added to the Result column, giving 8 as the Cube, and at the same time the constant 3rd Difference 6 is added to the 2nd Difference column, making it 12. These two additions are effected by the simultaneous adding of the 2nd to the 1st column, and of the 4th to the 3rd; the even columns being added to the odd ones in this first of the two double-strokes that form a complete operation. This is followed in the second double-stroke by adding the odd column (3rd) to the even one (2nd), the altered 2nd Difference 12, being added to the 1st Difference 7, making it 19, and the Natural-number 1 is advanced to 2 corresponding to the Cube 8. In the 3rd Calculation the altered 1st Difference 19, is added to the Result column making it 27 as the cube of 3, the 3rd Difference 6 being at the same time added to the 2nd Difference 12, making it 18 and then by the second double-stroke, the Natural-number is advanced to 3, and the 1st Difference is increased to 37, which is the required number for adding to 27 to make 64 in the succeeding operation, as the Cube of 4.
The numbers consisting of two figures such as 12, are shown upon two dials, the lower one showing the units 2, and the upper one the tens 1, but in advancing from 6 to 12, (as in the addition of 6 to the 2nd difference column in the 2nd calculation) the lower dial is advanced from 6 to 7, 8, 9, successively and then on to 0, 1, 2, where it remains stationary at. 2 ; and a separate provision is required for carrying 1 from the lower units dial to the upper tens dial, in order that the result may read 12 instead of only 2. This carrying process is effected by a contrivance of special mechanical interest, which provides not only for the carrying of the 10's from each dial to the one above, but also for the second carrying of 10 to the next dial still higher, which is rendered necessary by the act of carrying from the dial below whenever the upper one happens to be already at 9, so that it becowes advanced to 10 by the act of carrying from the dial below; and this further secondary carrying is effected if required throughout the entire height of the column. All these carryings are effected in the forward strokes the handle from back to front, between each of the two backward strokes from front to back by which the adding is effected in each complete double-stroke of the handle; the first of the two forward strokes effects all time primary carryings, and the second one picks up and completes all the secondary carryings that may be caused by the results of the primary carrying.
These carrying operations illustrate the principle upon which the whole action of the machine is designed, namely, arranging the several movements so that they follow one another successively without any possibility of interference between different movements as the several portions of the machinery take up the work one from one another in fixed order of succession,each movement being absolutely terminated before any other can possibly be commenced in the same portion of the machine. At. the same time an important economy is effected in the total time required for each calculation by carrying on simultaneously different operations that do not interfere with one another; and great mechanical skill and ingenuity is displayed in the means by which the time of each calculation has been shortened, and the whole machine made compact, by dovetailing together the numerous separate movements of the machine.
The mechanism for effecting the Process of Adding, though complicated in appearance, is essentially simple in principle. The driving handle is made to actuate two different portions of the machine in its backward and forward movements respectively ; as illustrated in Figs. 3 and 4, Plate 3, which are plans at the top of the machine, showing in each of them only such portions of the machinery as are concerned in the particular operation referred to in that Fig. The adding machinery is actuated by three wheels, I, I, I, fixed upon three vertical shafts in the centre of the machine, that extend the entire height; these wheels are geared together, moving in the directions shown by the arrows. The first wheel is connected to the driving handle E by means of the ratchet-pawl J, which is in gear with the rachet-wheel fixed upon the handle only during the backward movement of the handle from front to back, and slips round freely during the return foward movement of the handle. The adding wheels I, I, I, are consequently driven round during the backward movement of the handle, and then stand still during an equal time in the return forward movement.
The three vertical shafts upon which the figure dials are placed loosely in the front of the machine have three wheels K K K, fixed upon them at the top, which are geared together, and the middle one is driven through an intermediate connecting wheel L from a wheel M, fixed upon one of two vertical shafts N N, at the back of the machine. This wheel M is driven by the wheel O, that is fixed upon the spindle of the handle A, but the connection between the wheel M and the shaft N is though the ratchet-pawl P, which is in gear only during the forward movement of the handle from back to front, and slips round freely during the return movement, leaving the wheel M stationary during that. Time; (the ratchet-wheel P is carried upon a second loose wheel that is under the wheel M, and is in gear with the wheel O fixed upon the driving handle, as shown by the dotted circles.)
The adding wheels by means of which the successive additions are made to the front dials, are placed on the middle shafts I, I, at the back of the dials, and geared to them separately by means of a wheel fixed at the bottom of each dial. The adding wheels are all loose upon the shafts, but any of the wheels can be coupled to the shaft separately by means of a transverse locking bolt, one for each wheel, shown enlarged at R in Figs. 5, 6, and 7, Plate 4, which pass through boxes fixed upon the shafts and rotate with them. When these locking bolts are in their ordinary central position, each one revolves with the shaft. inside the notched rim of the wheel above without any action upon it.; but if the locking-bolt is shot by being pushed end ways, as shown in Figs. 5 and 6, the end of the bolt enters between projecting teeth on the wheel and locks the wheel to the shaft as shown at Q, causing the wheel to revolve with the shaft until the bolt is withdrawn again.
Each wheel that can be locked to the shaft in this way is in gear with the dial next above, so that the circumstance of any wheel being locked to the shaft would cause the dial above it to be turned completely round by the next stroke of the handle making it thus count or add 10. But this is prevented by the bolt being withdrawn before the end of the complete rotation, leaving the shaft to complete its rotation whilst the dial stands still during the remaining portion ; and this withdrawal of the bolt is effected exactly when the figure is reached in the rotation that is required to be added to the dial from the one below. Thus the process of adding is effected in the following manner : the machine endeavours to add 10 every time from each dial to the one above, but this adding is prevented taking effect except in those particular dials that require adding, and in those the adding process is only carried so far as the amount of the figure that is required to be added. The adding is arrested as soon as the desired figure is reached by the withdrawal of the bolt at that point, which leaves the shaft to complete its rotation without further action; and the adding of any figure -say 5- is effected by counting on to the upper dial all the successive figures 1, 2, 3, 4, until 5 is reached.
The means of withdrawing the locking bolt is by a pin on its underside S in Figs. 5 and 7, coming into contact with a wedge T upon the wheel below, as shown by the successive dotted positions of the pin S in Fig. 7. This is in gear with the corresponding lower dial and the position of this wedge determines the point (or figure) at which the bolt is withdrawn. The wedge is fixed upon the wheel at the position corresponding to 0 upon the dial, so that if the dial stands at 5, (or half way round towards 10), the wedge will be situated at a point half-way round, and will not come into contact with the withdrawing pin of the bolt until that has also travelled half-way round and has consequently carried forward the upper dial half-way round, or through a space of 5 figures, that is has made an addition of 5 to the upper dial; it is thus prevented from adding any more by the bolt being withdrawn by the action of the wedge, which takes place as soon as the figure 5 is reached that is required to be added.
The shooting of the locking bolt is is effected in the forward strokes of the handle, at the same time as the carrying process, and at the same time the wheels to be locked are all standing still, and all in the same position of 0, each one having completed its rotation. The bolts are shot, by means of arms upon the two vertical shafts N N in Fig. 4 at the back of the machine, the left-hand one of these is made to revolve by the handle as before shown, and the right-hand one is driven from the other by means of an intermediate wheel U, which causes the two shafts N N to rotate in the aune direction.
The revolving locking.arm V, as shown in Figs. 5 and 6, has a stud projecting downwards at the end, which acts on the bolt through an intermediate lever W that has a corresponding stud projecting upwards. The object of this intermediate lever W is to provide for the case of the lower dial happening to be at 0 at the time of the locking-arm being in action, when there should not be anything added to the upper dial; for if the locking-bolt were then shot as usual it. would begin to propel the wheel, and could not be withdrawn until it had already advanced the wheel from 0 to 1, and thereby erroneously added 1 to the upper dial. The ordinary shooting of the bolt has therefore to be prevented whenever the lower dial happens to be at 0, and this is effected by an ingenious arrangement which causes the intermediate lever W to be withdrawn at that time out of the range of action of the locking-arm ; so that although the locking-arm inmtkcs its regular stroke, and attempts to shoot the bolt as usual, it is prevented from acting on the locking-bolt by the absence of the intermediate lever through which it ordinarily acts. The intermediate lever is connected by a short vertical spindle to a corresponding lever X below, that is pressed by a spring against the circumference of the lower wheel; but this wheel has a projecting cam Y at the point corresponding with 0, which pushes out the lower lever when passing that point, as shown in Fig. 7, and so causes the upper intermediate lever to be similarly pushed out, so that the stud upon it then misses coming in contact with the stud on the locking-arm V (as shown by the dotted position in Fig. 5), and consequently, although the latter makes its stroke as usual, it produces no effect that time upon the locking-bolt.
It may be said to be a mechanical treat to watch the action of this mechanism, and observe how neatly and promptly the levers get out of the way whenever they are not required to act, and then return immediately afterwards to their regular position; and it has to be borne in mind that all the apparatus that has been described is multiplied many times over in the machine, and every portion is so skilfully arranged as to perform its work without.any risk of clashing with the movements of other parts. This is specially provided for by an elegant arrangement which ensures all the movements that could interfere at all, following one another in accurate succession, each movement being completed and absolutely stopped before the next one begins. This is effected by the several locking arms for shooting the bolts being arranged spirally round each revolving shaft, as shown at N N in the plan, Fig. 2, so that they come into action in succession, only one of them being in action at any one moment. This arrangement has also an important practical advantage, that the resistance opposed to the driving handle is distributed over the whole length of its stroke ; so that although a large number of separate movementts have to be effected during the stroke, only a gentle pull is required for working the handle, and the pull is nearly uniform throughout without any jerks to cause unsteadiness of motion. The rule in working the machine is that, no more than a gentle force is ever to be applied to move the handle, and if that should not be sufficient to move it at any time, the working is to be suspended until the accidental cause of the unusual resistance is ascertained and removed. The rate of moving the handle in ordinary working can be about 20 double strokes per minute.
The Carrying apparatus acts like the adding appparatus on the principle of having a power that is acting every time to the full extent, but only making use of it at the times that may be wanted.. For the purpose of carrying 1 to the wheel above in any case, that wheel has to be moved 1-10th of a revolution, and the wheel is made with 10 ratchet teeth, as shown at A in Fig. 9, Plate 5, into which a pawl B acts that is held on a carrying-arm C centred loosely upon the wheel shaft. This carrying arm is acted upon by a revolving picking-up arm D, fixed on the front vertical shaft K, Fig. 4, that makes an entire revolution each time, and if nothing were to intervene would effect a carrying of 1 at each revolution; but when the ratchet.pawl has been once driven forward in this way a distance of one tooth, it is held there by the retaining-hook E and thus prevented from returning to its original position where it. could be again acted on by the revolving picking-up arm, until that retaining-hook is released.
This releasing of the retaining-hook is effected by a projecting stud upon the dial below, F in Fig. 10, which acts upon an arm G fixed upon the spindle as the hook E, which stands at the position of 0 ; so that whenever the dial below comes to 0 showing that 10 is required to be carried by adding 1 to the dial above, the retaining-hook is then released, as shown in Fig. 10, the ratchet arm C returns to its original position, and the picking-up arm D then catches it in its next revolution and effects the required carrying. The ratchet-arm is carried back to its original position by a spring, and the release of th retaining -hook gives a click sound,that it is the "warning " that a carrying is about to take place ; and on watching the machine whilst in action, it is observed that whenever any dial comes to 0, showing that 10 is required to be carried, this "warning" is immediately heard, and is always followed in the return stroke of the handle by an advance of 1 in the dial above, showing that the 10 has been duly carried. The picking-up arms are arranged spirally (like the lockiug.arms previously described) so as to act in succession, beginning at the bottom, and by this means time is allowed for a warning to be given, and a carrying effected whenever an additional or secondary carrying is rendered necessary in any dial by the result of a carrying in the dial below.
The first object of this Difference Engine was to calculate those Tables (such as powers of numbers) in which a constant difference exists; but it is not limited in its application to such cases, and other tables (such as logarithms) though they cannot be reduced to a constant dillereaue, approximate more and more closely to one the farther the differences are carried out, and any desired extent of accuracy can be attained by carrying out the differences far enough. Babbage intended constructing by his complete machine (of which the existing one is only a small portion), a table of logarithms correct to 7 places of decimals, by means of working out the numbers to 20 places of decimals by the machine and using only the first 7 of these 20 for each final result.
During the progress of the construction of the "Difference Engine," he conceived the idea of in further extension to an "Analytical Engine" of greatly increased power, that could calculate the numerical value of any algebraical expression and then at any period of the series previously fixed upon or contingent upon certain events in the machine, would commence a different, calculation, and would he able to repeat such changes to any desired extent. The design of this extraordinary machine is stated to have been sufficiently advanced during the interval in the progress of the original machine was suspended, to have been susceptible of practical execution ; but it was never really commenced before the whole proceedings were abandoned.
Babbage's design of the original machine comprised an arrangement for automatic printing, by means or stamps struck upon a metal plate so as to form a stereotype for printing from direct, and to avoid all subsequent source of error from compositors' work and correcting of the press; but this is not included in the existing portion of the machine.
It has been only intended in this paper to give such a description of this remarkable machine as will convey an explanation of its general principle and action, without attempting to enter into all the details of construction that make it applicable for other special purposes. In the illustrations some of the details of the machine have been slightly modified for the purpose of explaining the action ware clearly, (the position of the locking-arms and the form of the intermediate lever, and the driving ratchet.wheel); also the under side instead of the upper side has been shown of some parts that are superposed. The adding wheels are made with twenty teeth instead of ten teeth, and turn only half round each time instead of an entire revolution.
As a general and comprehensive idea of the mode of action of the machine Babbage's own expression may be quoted - that there are two waves of motion flowing through the machine separately and alternately, one for adding and the other for carrying; the adding wave flowing transversely from left to right, and the carrying wave flowing vertically from bottom to top, the two waves following one another and becoming superposed, and their combined, result is carried forward, step by step, by each successive alternation of the waves.
Plate 1
Plate 2
Plate 3
Plate 4
Plate 5
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